{"id":24436,"date":"2020-06-24T11:23:16","date_gmt":"2020-06-24T02:23:16","guid":{"rendered":"https:\/\/www.ibaraki-ct.ac.jp\/?p=24436"},"modified":"2023-07-31T18:09:24","modified_gmt":"2023-07-31T09:09:24","slug":"%e3%83%97%e3%83%ac%e3%82%b9%e3%83%aa%e3%83%aa%e3%83%bc%e3%82%b9-%e7%a0%94%e7%a9%b6%e6%88%90%e6%9e%9c%e7%99%ba%e8%a1%a8%ef%bc%88%e4%bc%8a%e8%97%a4%e4%b8%80%e8%88%ac%e6%95%99%e9%a4%8a%e9%83%a8","status":"publish","type":"post","link":"https:\/\/www.ibaraki-ct.ac.jp\/info\/archives\/24436","title":{"rendered":"[\u30d7\u30ec\u30b9\u30ea\u30ea\u30fc\u30b9] \u7814\u7a76\u6210\u679c\u767a\u8868\uff08\u4f0a\u85e4\u4e00\u822c\u6559\u990a\u90e8\u8b1b\u5e2b\uff09"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"> <strong>\u65b0\u305f\u306a\u7d50\u3073\u76ee\u7406\u8ad6\u3067\u300c\u5fae\u5206\u300d\u306e\u6982\u5ff5\u3092\u5237\u65b0<\/strong><br> <strong>\u2014\u570f\u8ad6\u5316\u306b\u3088\u308b\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc\u3067\u91cf\u5b50\u8ad6\u3078\u306e\u66f4\u306a\u308b\u5fdc\u7528\u304c\u671f\u5f85\u2014<\/strong>  <br><\/h2>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><br><strong>\u672c\u6821\u6559\u54e1\u3068\u6771\u5927\u7814\u7a76\u54e1\u306e\u30da\u30a2\u300120\u5e74\u306e\u6c88\u9ed9\u3092\u7834\u308b\u7d50\u679c\u3092\u51fa\u3059<\/strong><br><br><\/h2>\n\n\n\n<p style=\"font-size:25px\" class=\"has-text-align-right wp-block-paragraph\">\uff12\uff10\uff12\uff10\u5e74\uff16\u6708\uff12\uff14\u65e5<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/01kosen-I.png\" alt=\"\" class=\"wp-image-24041\" width=\"428\" height=\"70\"\/><\/figure><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p style=\"font-size:25px\" class=\"has-text-align-right wp-block-paragraph\">\u72ec\u7acb\u884c\u653f\u6cd5\u4eba\u56fd\u7acb\u9ad8\u7b49\u5c02\u9580\u5b66\u6821<br>\u8328\u57ce\u5de5\u696d\u9ad8\u7b49\u5c02\u9580\u5b66\u6821<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-size:22px\">\u3010\u6982\u8981\u3011<br> \u7d10\u5168\u4f53\u306e\u69cb\u9020\u3092\u8abf\u3079\u308b\u306e\u306b\u6709\u52b9\u306a\u5fae\u5206\u7406\u8ad6\u304c21\u4e16\u7d00\u306e\u91cf\u5b50\u8ad6\u306b\u5bfe\u5fdc\u3057\u3066\u3001\u3069\u306e\u3088\u3046\u306b\u89b3\u5bdf\u30fb\u89b3\u6e2c\u3055\u308c\u308b\u304b\u3042\u3089\u3086\u308b\u79d1\u5b66\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3067\u3057\u305f\u3002\u3068\u3053\u308d\u304c\u3001\u305d\u308c\u306f\u91cf\u5b50\u6b21\u6570\u3068\u3044\u3046\u3082\u306e\u3092\u52d5\u304b\u3055\u306a\u3044\u300c\u7d10\u306e\u4ea4\u5dee\u4ea4\u63db[mfn]\u300c\u7d10\u306e\u63a5\u304e\u66ff\u3048\u300d\u306e\u9805\u3092\u53c2\u7167\u306e\u3053\u3068\u3002[\/mfn]\u300d(\u7d10\u306e\u63a5\u304e\u66ff\u3048[mfn]\uff12\u3064\u306e\u7d10\u3092\u4f7f\u3063\u3066\u673a\u306a\u3069\u306b\u5341\u5b57\u3092\u91cd\u306d\u3066\u4ea4\u5dee\u3092\u4f5c\u308b\u3068\u304d\u3001\u3053\u306e\u4ea4\u5dee\uff11\u3064\u306b\u5bfe\u3057\u3066\u3001\u4ea4\u5dee\u3092\u306a\u3059\u7d10\u306e\u4e0a\u4e0b\u3092\u63a5\u304e\u66ff\u3048\u306b\u3088\u308a\u5165\u308c\u66ff\u3048\u308b\u3053\u3068\u3092\u5c02\u9580\u7528\u8a9e\u3067\u300c\u4ea4\u5dee\u4ea4\u63db\u300d\u3068\u3044\u3046\u3002\u8a00\u3044\u63db\u3048\u308b\u306a\u3089\u3001\u7d10\u306e\u63a5\u304e\u66ff\u3048\u3001\u3067\u3042\u308b\u3002[\/mfn])\u306b\u304a\u3051\u308b\u7a7a\u9593\u5217\u3060\u3068\u3044\u3046\u3053\u3068\u3092\u3001\u4eca\u56de\u3001\u6570\u5b66\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u7a81\u304d\u6b62\u3081\uff08\u56f3\uff11\u306e\u4e09\u89d2\u69cb\u9020\uff09\u3001\u3055\u3089\u306b\u306f\u7269\u7406\u91cf\u3068\u306a\u308b\u65b0\u3057\u3044\u300c\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc [mfn]\u7d50\u3073\u76ee\u306e\u95a2\u6570\u304c\u3001\u7d50\u3073\u76ee\u3092\u5165\u529b\u3059\u308b\u3068\u6570\u3092\u5024\u3068\u3057\u3066\u3068\u308b\u306e\u306b\u5bfe\u3057\u3001\u7d50\u3073\u76ee\u306e\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306f\u7d50\u3073\u76ee\u3092\u5165\u529b\u3059\u308b\u3068\u3001\u300c\u6570\u306e\u7a7a\u9593\u300d\u3092\u8fd4\u3059\u3002\u6570\u306e\u7a7a\u9593\u306f\u3001\u901a\u5e38\u306f\u6574\u6570\u5168\u4f53\u306e\u96c6\u5408\u3092\u3044\u304f\u3064\u304b\u7d44\u307f\u306b\u3057\u305f\u3082\u306e\u3067\u8a18\u8ff0\u3055\u308c\u308b\u3002\u300c\u30db\u30e2\u30ed\u30b8\u30fc\u300d\u306e\u9805\u76ee\u3067\u8aac\u660e\u3057\u305f\u3088\u3046\u306b\u3001\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc\u306f\u3001\u7d50\u3073\u76ee\u306e\u5e7e\u4f55\u7684\u306a\u7279\u5fb4\u3092\u6349\u3048\u308b\u3002\u672c\u8ad6\u6587\u3067\u306f\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc\u306e\u65b0\u3057\u3044\u7d44\u307f\u4e0a\u3052\u69cb\u9020\u3092\u8003\u6848\u3057\u3001\u7d50\u3073\u76ee\u3088\u308a\u3082\u5e83\u3044\u5bfe\u8c61\u306e\u65b0\u3057\u3044\u30db\u30e2\u30ed\u30b8\u30fc\u3092\u4e16\u306e\u4e2d\u306b\u4e0e\u3048\u305f\u3002[\/mfn] \u300d\u3092\u767a\u898b\u3057\u307e\u3057\u305f\uff08\u56f31\u306e\u300cH\u300d\uff09\u3002 <\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/e6d032794c5d4593438b7d4042796636-1024x517.png\" alt=\"\" class=\"wp-image-24037\" width=\"1024\" height=\"517\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-size:22px\"><br>\u3010\u3053\u306e\u30ea\u30ea\u30fc\u30b9\u306e\u30dd\u30a4\u30f3\u30c8\u3011<br>(1) \u79d1\u5b66\u3067\u306f\u91cd\u8981\u306a\u300c\u7d10\u306e\u7a7a\u9593\u69cb\u9020\u300d\u3092\u8abf\u3079\u308b\u305f\u308120\u4e16\u7d00\u3067\u306f\u300c\u7d50\u3073\u76ee  [mfn]  \u9589\u3058\u305f\uff11\u672c\u306e\u7d10\u306e\u3053\u3068\u3002\u7269\u7406\u5b66\u3001\u5316\u5b66\u3001\u751f\u7269\u5b66\u306b\u73fe\u308c\u308b\u3002\u76f4\u63a5\u7d10\u306b\u306a\u3063\u3066\u3044\u306a\u304f\u3066\u3082\u98db\u884c\u6a5f\u306e\u7ffc\u7aef\u306e\u6e26\u3084\u5b87\u5b99\u7a7a\u9593\u306e\u4ea4\u5dee\u7a7a\u9593\u3092\u7d50\u3073\u76ee\u3060\u3068\u3044\u3046\u3053\u3068\u3082\u3042\u308b\u3002\u65e5\u672c\u3067\u306f\u9ad8\u5206\u5b50\u3084DNA\u306b\u304a\u3051\u308b\u7d50\u3073\u76ee\u7406\u8ad6\u7814\u7a76\u304c\u6d3b\u767a\u3067\u3042\u308b\u3002  [\/mfn]  \u306e\u95a2\u6570\u3084\u5fae\u5206\u300d\u304c\u4f7f\u308f\u308c\u3066\u304d\u305f\u3002<br>(2)  21\u4e16\u7d00\u3001\u570f\u8ad6 [mfn] \u6570\u5b66\u306e\u57fa\u790e\u3092\u76f8\u5bfe\u7684\u306a\u95a2\u4fc2\u6027\u306b\u3088\u308a\u5b9a\u7fa9\u30fb\u69cb\u7bc9\u3057\u3001\u8003\u3048\u3066\u3044\u308b\u6570\u5b66\u306e\u5bb9\u308c\u7269\u3068\u81ea\u5206\u304c\u8003\u3048\u3066\u3044\u308b\u7acb\u5834\u3092\u660e\u78ba\u306b\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u3001\u6570\u5b66\u306e\u4e00\u5206\u91ce\u3002\u8003\u5bdf\u3057\u3066\u3044\u308b\uff12\u3064\u306e\u6570\u5b66\u3092\u6709\u52b9\u306b\u95a2\u9023\u4ed8\u3051\u3001\u4e92\u3044\u306e\u6570\u5b66\u306b\u5fdc\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002 [\/mfn] \u5316\u3068\u547c\u3070\u308c\u308b\u624b\u6cd5\u306b\u3088\u308a\u7d50\u3073\u76ee\u306e\u95a2\u6570\u3092\u7d71\u5236\u3059\u308b\u300c\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc\u300d\u304c\u767a\u898b\u3055\u308c\u305f\u3002 <br>(3)  \u4eca\u56de\u300121\u4e16\u7d00\u306e\u65b9\u6cd5\u306b\u3088\u308a20\u4e16\u7d00\u7684\u306a\u300c\u7d10\u306e\u5fae\u5206\u7406\u8ad6\u300d\u304c\u3069\u306e\u3088\u3046\u306b\u6349\u3048\u3089\u308c\u308b\u304b\u3092\u6570\u5b66\u306b\u3088\u3063\u3066\u521d\u3081\u3066<br>\u3000\u7a81\u304d\u3068\u3081\u305f\u3002<\/p>\n\n\n\n<p><div style=\"border: 5px solid #87cefa; padding: 10px; border-radius: 0px; background: ##ffffff;\"><span style=\"font-size: large;\">\u3010\u89e3\u8aac\u30b3\u30e9\u30e0\uff1a\u570f\u8ad6\u5316 (\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3) \u306e\u5229\u70b9\u3011<br><br>\u6570\u5b66\u306b\u304a\u3051\u308b\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u5177\u4f53\u4f8b\u3068\u3057\u3066\u8fd1\u5e74\u6700\u3082\u6ce8\u76ee\u3092\u6d74\u3073\u305f\u3082\u306e\u304c\u3001\u30b8\u30e7\u30fc\u30f3\u30ba\u591a\u9805\u5f0f[mfn]1984\u5e74\u9803\u306b\u4f5c\u7528\u7d20\u74b0\u8ad6\u3068\u547c\u3070\u308c\u308b\u5206\u91ce\u304b\u3089\u898b\u51fa\u3055\u308c\u305f\u7d50\u3073\u76ee\u4e0d\u5909\u91cf\u3002\u30b8\u30e7\u30fc\u30f3\u30ba\uff081990\u5e74\u306b\u30d5\u30a3\u30fc\u30eb\u30ba\u8cde\u53d7\u8cde\uff09\u304c\u767a\u898b\u3057\u305f\u3002\u306a\u304a\u3001\u7d50\u3073\u76ee\u91cf\u5b50\u4e0d\u5909\u91cf\u3068\u3057\u3066\u3001\u307e\u305f\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u306b\u3088\u308a\u518d\u5b9a\u5f0f\u5316\u304c\u306a\u3055\u308c\u3001\u91cf\u5b50\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5909\u6570\u3068\u3057\u3066\u6301\u3064\u3002[\/mfn]\u306e\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u30db\u30d0\u30ce\u30d5\uff08Khovanov, \u73fe\u30b3\u30ed\u30f3\u30d3\u30a2\u5927\u5b66\u6559\u6388\uff09\u306b\u3088\u308a2000\u5e74\u306b\u767a\u8868\u3055\u308c\u5927\u304d\u306a\u6ce2\u53ca\u52b9\u679c\u304c\u3042\u3063\u305f\u3002\u7279\u306b\u4ee5\u4e0b\u306e\u30e1\u30ea\u30c3\u30c8\u304c\u77e5\u3089\u308c\u3066\u3044\u308b\u3002<br><br>\u25a0\u3000\u7d50\u3073\u76ee\u306e\u30b8\u30e7\u30fc\u30f3\u30ba\u591a\u9805\u5f0f\u3092\u7d14\u7c8b\u306b\u4e00\u822c\u5316\u3057\u3066\u3044\u308b\u69d8\u5b50\u304c\u308f\u304b\u308a\u3084\u3059\u3044\u3002<br><br>\u25a0\u3000\u5206\u91ce\u6a2a\u65ad\u7684\u306b\u3088\u304f\u7528\u3044\u3089\u308c\u308b\u30d5\u30ed\u30d9\u30cb\u30a6\u30b9(Frobenius)\u4ee3\u6570\u3068\u5bfe\u5fdc\u3059\u308b (1+1) TQFT\uff08\u4f4d\u76f8\u7684\u5834[mfn]\u91cf\u5b50\u8ad6\u306b\u3088\u308c\u3070\u3001\u7a7a\u9593\u5185\u3092\u98db\u3073\u56de\u308b\u7c92\u5b50\u306f\u3001\u7a7a\u9593\u5185\u306b\u5e83\u304c\u308b\u300c\u72b6\u614b\u300d\u3068\u307f\u306a\u3055\u308c\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u8a2d\u5b9a\u3092\u6570\u5b66\u516c\u7406\u7cfb\u3068\u3057\u3066\u8a18\u8ff0\u3057\u305f\u3082\u306e\uff081966\u5e74\u306e\u30d5\u30a3\u30fc\u30eb\u30ba\u8cde\u53d7\u8cde\u8005\u306e\u30a2\u30c6\u30a3\u30e4\u306b\u3088\u308b\uff09\u304c\u4f4d\u76f8\u7684\u5834\u306e\u7406\u8ad6\u3067\u3042\u308b\u3002\u300c\u72b6\u614b\u300d\u3092\u6349\u3048\u308b\u7a7a\u9593\u3092\u6642\u9593\u767a\u5c55\u3055\u305b\u305f\u3001\u3088\u308a\u5e83\u3044\u7a7a\u9593\uff08\u5c02\u9580\u7528\u8a9e\u3067\u306f\u300c\u30b3\u30dc\u30eb\u30c7\u30a3\u30ba\u30e0\u300d\uff09\u3092\u6570\u5b66\u3067\u6271\u3048\u308b\u3088\u3046\u306b\u306a\u308b\u3002\u672c\u8ad6\u6587\u3067\u306f\u3053\u306e\u7406\u8ad6\u304c\u99c6\u4f7f\u3055\u308c\u305f\u3002[\/mfn]\u306e\u91cf\u5b50\u8ad6, Topological Quantum Field Theory\uff09\u3092\u4f7f\u3063\u3066\u69cb\u6210\u3055\u308c\u3066\u304a\u308a\u6271\u3044\u3084\u3059\u3044\u3002<br><br>\u25a0\u3000\u306f\u3063\u304d\u308a\u3068\u3057\u305f\u5fdc\u7528\u304c\u3042\u308b\u3002\u7269\u7406\u5b66&#8211;\u3088\u308a\u6d17\u7df4\u5316\u3055\u308c\u305f\u30c1\u30e3\u30fc\u30f3\u30fb\u30b5\u30a4\u30e2\u30f3\u30ba\u7406\u8ad6\u306e\u30e2\u30c7\u30eb\u3084\u771f\u7a7a\u72b6\u614b\u306e\u8a18\u8ff0\u3002\u6570\u5b66&#8211;\u30b8\u30e7\u30fc\u30f3\u30ba\u591a\u9805\u5f0f\u3067\u533a\u5225\u3067\u304d\u306a\u3044\u30da\u30a2\u3092\u533a\u5225\u3059\u308b \/ \u30df\u30eb\u30ca\u30fc\u4e88\u60f3\u306e\u7c21\u6613\u306a\u5225\u8a3c\u660e\u3002\uff08\u4eca\u56de\u306e\u95a2\u9023\u3067\u306f\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u3078\u306e\u5fdc\u7528\u3068\u3057\u3066\u4f0a\u85e4\u6607\u306e2011\u5e74\u306e\u30db\u30d0\u30ce\u30d5\u30db\u30e2\u30ed\u30b8\u30fc[mfn]2000\u5e74\u9803\u306b\u30db\u30d0\u30ce\u30d5\u304c\u767a\u898b\u3057\u305f\u3002\u30b8\u30e7\u30fc\u30f3\u30ba\u591a\u9805\u5f0f\u3092\u91cf\u5b50\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u6b21\u6570\u3054\u3068\u306b\u6574\u7406\u3057\u305f\u3068\u304d\u3001\u5404\u4fc2\u6570\u3092\u30aa\u30a4\u30e9\u30fc\u6570\u3068\u3059\u308b\u3088\u3046\u306a\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u304c\u5bfe\u5fdc\u3059\u308b\u4e0a\u90e8\u69cb\u9020\u3092\u6301\u305f\u305b\u308b\u4ed5\u7d44\u307f\u3002\u3053\u306e\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306f\u7d50\u3073\u76ee\u4e0d\u5909\u91cf\u3068\u306a\u3063\u3066\u3044\u308b\u3002[\/mfn]\u306b\u95a2\u3059\u308b\u8ad6\u6587\uff08N.Ito, 2011\uff09\u304c\u91cf\u5b50\u7b26\u53f7\u7406\u8ad6\u306b\u6d3b\u7528 (Audoux, 2014)\u3055\u308c\u3066\u3044\u308b\u3002\uff09<\/span><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><br><br>\u300c\u7d50\u3073\u76ee\u306e\u4ea4\u5dee\u4ea4\u63db\u300d\u3068\u3044\u3046\u57fa\u672c\u7684\u3067\u6c4e\u7528\u6027\u304c\u9ad8\u3044\u5e7e\u4f55\u7684\u306a\u624b\u8853\u3001\u300c\u7d10\u306e\u5c40\u6240\u7684\u306a\u4ea4\u5dee\u4ea4\u63db\u300d\uff08\u56f31\u5de6\uff09\u306f\u3001\u7d50\u3073\u76ee\u306e\u8907\u96d1\u3055\u3092\u6e2c\u308b\u4e0a\u3067\u306e\u91cd\u8981\u306a\u53e4\u5178\u7684\u4e0d\u5909\u91cf\u3067\u3042\u308b\u300c\u7d50\u3073\u76ee\u89e3\u6d88\u6570\u300d\u3092\u5b9a\u7fa9\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u7d50\u3073\u76ee\u91cf\u5b50\u4e0d\u5909\u91cf  [mfn] \u91cf\u5b50\u7fa4\u3068\u547c\u3070\u308c\u308b\u3001\u91cf\u5b50\u5316\u3055\u308c\u305f\u7a7a\u9593\u306e\u69cb\u9020\u3092\u7528\u3044\u3066\u4f5c\u3089\u308c\u305f\u7d50\u3073\u76ee\u4e0d\u5909\u91cf\u306e\u3053\u3068\u3002\u306a\u304a\u3001\u91cf\u5b50\u7fa4\u306f\u795e\u4fdd\u9053\u592b\u3068\u30c9\u30ea\u30f3\u30d5\u30a7\u30eb\u30c8\u306b\u3088\u308a\u3001\u72ec\u7acb\u306b\u767a\u898b\u3055\u308c\u305f\u3002\u307e\u305f\u3001\u30c9\u30ea\u30f3\u30d5\u30a7\u30eb\u30c8\u306f1990\u5e74\u306e\u30d5\u30a3\u30fc\u30eb\u30ba\u8cde\u53d7\u8cde\u8005\u3002    [\/mfn] \u306e\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f[mfn] \u95a2\u6570f\u3001\u4ea4\u5dee\u4ea4\u63db\uff11\u3064\u306b\u5bfe\u3057\u3001\u6b21\u306e\u5f62\u306e\u95a2\u4fc2\u5f0f\u306e\u3053\u3068\u3092\u3044\u3046\u3002 <br>f(\u4e0a\u306b\u306a\u3063\u305f\u7d10\u306e\u72b6\u614b) \u2013 f(\u4e0b\u306b\u306a\u3063\u305f\u7d10\u306e\u72b6\u614b) = f(\u4e2d\u9014\u72b6\u614b\u306e\u7279\u7570\u7d50\u3073\u76ee).  <br> \u4e00\u822c\u306b\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u3068\u3044\u3046\u3068\u304d\u306f\u3001\u4e0a\u8a18\u306e\u3088\u3046\u306a\u5f62\uff08\uff13\u9805\u3067\u3042\u308b\u3068\u304b\u5358\u7d14\u306a\u5f15\u304d\u7b97\uff09\u3068\u306f\u9650\u3089\u305a\u3001\u307e\u305f\u300c\u4e2d\u9014\u72b6\u614b\u300d\u3092\u7528\u3044\u305a\u7d50\u3073\u76ee\/\u7d61\u307f\u76ee\u3060\u3051\u3067\u69cb\u6210\u3055\u308c\u308b\u3082\u306e\u3092\u6307\u3059\u3053\u3068\u304c\u591a\u3044\u3002\u672c\u8ad6\u6587\u3067\u306f\u30d0\u30b7\u30ea\u30a8\u30d5\u306e\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u306b\u80cc\u5f8c\u69cb\u9020\u304c\u4ed8\u52a0\u3055\u308c\u3001\u65b0\u305f\u306a\u610f\u5473\u4ed8\u3051\u304c\u306a\u3055\u308c\u305f\u3002\u8a00\u3044\u63db\u3048\u308b\u306a\u3089\u3001\u672c\u8ad6\u6587\u3067\u3053\u306e\u95a2\u4fc2\u5f0f\u304c\u4e16\u754c\u3067\u521d\u3081\u3066\u570f\u8ad6\u5316\u3055\u308c\u305f\u3002 <br> [\/mfn]\uff08\u91cf\u5b50\u7fa4\u306b\u304a\u3051\u308bR-\u884c\u5217\u306e\u5dee\u306b\u3088\u3063\u3066\u5c0e\u304b\u308c\u308b\u3082\u306e\uff09\u3092\u8a18\u8ff0\u3059\u308b\u3082\u306e\u3068\u3057\u3066\u3082\u91cd\u8981\u3067\u3059\u3002\u4e2d\u3067\u3082\u30d0\u30b7\u30ea\u30a8\u30d5 (Vassiliev)\u4e0d\u5909\u91cf\u306e\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u3084\u30a2\u30ec\u30af\u30b5\u30f3\u30c0\u30fc\u30fb\u30b3\u30f3\u30a6\u30a7\u30a4(Alexander-Conway)\u591a\u9805\u5f0f\u306f\u4ea4\u5dee\u4ea4\u63db\u306e\u5358\u7d14\u306a\u5dee\u306b\u3088\u308a\u8a18\u8ff0\u3055\u308c\u307e\u3059\uff08\u4eca\u56de\u306e\u8ad6\u6587\u3067\u306e\u30d0\u30b7\u30ea\u30a8\u30d5\u4e0d\u5909\u91cf [mfn]\u672c\u8ad6\u6587\u306e\u4e3b\u5f79\u306e\uff11\u3064\u3002\u7d50\u3073\u76ee\u5168\u4f53\u304c\u306a\u3059\u96c6\u5408\u3092\u3001\u7279\u7570\u7d50\u3073\u76ee\u3092\u4f7f\u3044\u5206\u985e\u3059\u308b\u4ed5\u7d44\u307f\u3092\u6301\u3064\u300c\u4e0d\u5909\u91cf\u306e\u30bf\u30a4\u30d7\u300d\uff08\u30d0\u30b7\u30ea\u30a8\u30d5\u578b\u3068\u547c\u3070\u308c\u308b\uff09\u306e\u3053\u3068\u3092\u6307\u3057\u3001\u5177\u4f53\u7684\u306a\u7d50\u3073\u76ee\u4e0d\u5909\u91cf\u3068\u306f\u4e00\u7dda\u3092\u753b\u3059\u3002\u30d0\u30b7\u30ea\u30a8\u30d5\u578b\u3067\u3042\u308b\u3053\u3068\u306f\u3001\u30d0\u30b7\u30ea\u30a8\u30d5\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\uff08\u672c\u8ad6\u6587\u304c\u570f\u8ad6\u5316\u3057\u305f\u95a2\u4fc2\u5f0f\uff09\u3092\u4f7f\u3063\u3066\u78ba\u304b\u3081\u3089\u308c\u308b\u3002\u7570\u306a\u308b\u7d50\u3073\u76ee\u306e\u91cf\u5b50\u4e0d\u5909\u91cf\u3067\u3042\u3063\u3066\u3082\u3001\u91cf\u5b50\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u300c\u5fae\u5206\u306b\u3088\u3063\u3066\u6b63\u898f\u5316\u300d\u3059\u308b\u3068\u4fc2\u6570\u306b\u30d0\u30b7\u30ea\u30a8\u30d5\u4e0d\u5909\u91cf\u304c\u73fe\u308c\u308b\u3002\u3053\u306e\u666e\u904d\u6027\u304c\u6709\u540d\u3067\u3042\u308b\u3002\u95a2\u6570\u3068\u3057\u3066\u8a08\u7b97\u52b9\u7387\u304c\u826f\u3044\u3053\u3068\u3067\u3082\u77e5\u3089\u308c\u308b\u3002\u95a2\u6570\u306e\u5fae\u5206\u306b\u3088\u308b\u6b63\u898f\u5316\u306f\u9ad8\u5c022\u5e74\u3067\u7fd2\u3046\u3002  [\/mfn]  \u306e\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u306f\u56f31\u53f3\uff09\u3002<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/795316b92fc766b0181f6fef074f03fa-1024x130.png\" alt=\"\" class=\"wp-image-24038\" width=\"579\" height=\"73\"\/><\/figure><\/div>\n\n\n\n<p style=\"font-size:18px\" class=\"has-text-align-center wp-block-paragraph\">\u56f3\uff11<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> \u7279\u306b\u7d50\u3073\u76ee\u91cf\u5b50\u4e0d\u5909\u91cf\u306e\u91cf\u5b50\u30d1\u30e9\u30e1\u30fc\u30bf\u30fcq\u306e\u30c6\u30fc\u30e9\u30fc\u5c55\u958b\u306e\u5404\u6b21\u4fc2\u6570\u306f\u3069\u308c\u3082Vassiliev\u4e0d\u5909\u91cf\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u306b\u3088\u308a\u91cf\u5b50\u7fa4\u3092\u53f8\u308b\u30ea\u30fc(Lie)\u4ee3\u6570\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3068\u3044\u3046\u610f\u5473\u3067\u3001Vassiliev\u4e0d\u5909\u91cf\u306f\u666e\u904d\u7684\u3067\u3059\u3002 <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/2b530e80c7d0de90885e285c5d798063-1024x326.png\" alt=\"\" class=\"wp-image-24039\"\/><\/figure>\n\n\n\n<p style=\"font-size:18px\" class=\"has-text-align-center wp-block-paragraph\">\u56f3\uff12<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">\u3010\u80cc\u666f\u3011<br> \u73fe\u5728\u3001\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3 [mfn]\u53b3\u5bc6\u306a\u6570\u5b66\u7684\u306a\u5b9a\u7fa9\u306f\u306a\u304f\u6570\u5b66\u306e\u4e0a\u90e8\u69cb\u9020\u3092\u8868\u3059\u30ad\u30fc\u30ef\u30fc\u30c9\u3002\u4f8b\u3048\u30701 \u30012 \u30013\u306b\u5bfe\u30571\u6b21\u5143\u7a7a\u9593\u30012\u6b21\u5143\u7a7a\u9593\u30013\u6b21\u5143\u7a7a\u9593\u306e\u5217\u3092\u60f3\u8d77\u3057\u3001\u5143\u306f\u5358\u306b\u300c3\u3064\u306e\u6570\u300d\u3067\u3042\u3063\u305f\u3082\u306e\u306b\u6df1\u3044\u610f\u5473\u3084\u69cb\u9020\u3092\u6301\u305f\u305b\u308b\u3053\u3068\u3002\u672c\u8ad6\u6587\u306e\u4e3b\u5f79\u306e\u4e00\u3064\u3067\u3042\u308b\u3002  [\/mfn] \u3068\u3044\u3046\u8003\u3048\u65b9\u306f\u591a\u65b9\u9762\u306e\u6570\u5b66\u3067\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u304c\u5e83\u304f\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\uff08\uff08\u6df1\u8c37\uff0c2016\uff09\u304a\u3088\u3073\u300c\u30c1\u30e3\u30fc\u30f3\u8cde\u67cf\u539f\u6b63\u6a39\u6c0f\u304c\u53d7\u8cde\u300d\uff08\u300e\u65e5\u7d4c\u30b5\u30a4\u30a8\u30f3\u30b9\u300f\uff0c2018\u5e7410\u6708\u53f7\uff09\uff09\u3002\u305d\u3057\u3066\u5b9f\u969b\u306b\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3 \u3092\u5fdc\u7528\u3059\u308b\u7814\u7a76\u306f\u4eca\u3084\u4e16\u754c\u7684\u306b\u3068\u3066\u3082\u591a\u3044\u3053\u3068\u304c\u4e8b\u5b9f\u3068\u3057\u3066\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u4e00\u65b9\u3067\u3001\u305d\u306e\u6ce2\u53ca\u52b9\u679c\u3068\u306f\u88cf\u8179\u306b\u3001\u6709\u52b9\u306a\u30ab\u30c6\u30b4\u30ea\u30d5\u30a3\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u3059\u308b\u306e\u306f\u96e3\u6613\u5ea6\u304c\u9ad8\u3044\u3053\u3068\u3082\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u6545\u3001\u30db\u30d0\u30ce\u30d5\u7406\u8ad6\u304c\u59cb\u307e\u3063\u3066\u304b\u308920\u5e74\u3092\u7d4c\u3066\u30821990\u5e74\u4ee3\u306e\u30d0\u30b7\u30ea\u30a8\u30d5\u7406\u8ad6\u30682000\u5e74\u4ee3\u306e\u30db\u30d0\u30ce\u30d5\u7406\u8ad6\u3092\u6709\u6a5f\u7684\u306b\u7d50\u3073\u3064\u3051\u3066\u6d3b\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\u306b\u3044\u307e\u3057\u305f\u3002 <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/c8856789ec11ab8b1013037cef6929f9-1024x241.png\" alt=\"\" class=\"wp-image-24040\"\/><\/figure>\n\n\n\n<p style=\"font-size:18px\" class=\"has-text-align-center wp-block-paragraph\">\u56f3\uff13\uff08\u4e80\u5c71.2017\uff09\u306b\u57fa\u3065\u304f\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">\u3010\u4eca\u56de\u306e\u6210\u679c\u3011<br>\u672c\u7814\u7a76\u3067\u306f\u30db\u30d0\u30ce\u30d5\u30db\u30e2\u30ed\u30b8\u30fc\u4e0a\u3067\u300c\u7d50\u3073\u76ee\u306e\u4ea4\u5dee\u4ea4\u63db\u300d\u3092\u5b9f\u73fe\u3057\u3001\u30d0\u30b7\u30ea\u30a8\u30d5\u306e\u30b9\u30b1\u30a4\u30f3\u95a2\u4fc2\u5f0f\u306b\u304a\u3051\u308b\u5f15\u304d\u7b97\u3092\u56de\u5fa9\u3057\u9577\u5b8c\u5168\u5217\u3092\u5185\u5305\u3059\u308b\u30db\u30d0\u30ce\u30d5\u30db\u30e2\u30ed\u30b8\u30fc\u306b\u62e1\u5f35\u3057\u307e\u3057\u305f\u3002\u4ea4\u5dee\u4ea4\u63db\u3092\u4e0e\u3048\u308b\u30db\u30d0\u30ce\u30d5\u8907\u4f53(complex)\u4e0a\u306e\u5199\u50cf\uff08\u5217\uff09\u306f\u4f4d\u76f8\u7684\u306a\u4e0d\u5909\u6027\u3092\u6e80\u305f\u3057\u7279\u7570\u7d50\u3073\u76ee(singular link)  [mfn] \u4ea4\u5dee\u4ea4\u63db\u304c\u884c\u308f\u308c\u308b\uff12\u3064\u306e\u7d50\u3073\u76ee\u540c\u58eb\u306e\u300c\u4e2d\u9593\u4f53\u300d\u306b\u76f8\u5f53\u3059\u308b\u3082\u306e\u3002\u5c40\u6240\u7684\u306b\u4e00\u65b9\u306e\u7d10\u304c\u4ed6\u65b9\u306e\u7d10\u3092\u6a2a\u65ad\u3059\u308b\u3068\u304d\u306b\u73fe\u308c\u308b\uff12\u91cd\u70b9\uff08\u7279\u7570\u70b9\uff09\u3092\u3082\u3064\u3002 [\/mfn]  \u306e\u30db\u30d0\u30ce\u30d5\u30db\u30e2\u30ed\u30b8\u30fc\u3092\u5c0e\u304d\u307e\u3059\u3002\u3053\u306e\u30db\u30e2\u30ed\u30b8\u30fc   [mfn]   \u6570\u5b66\u306e\u5404\u5206\u91ce\u306b\u767b\u5834\u3059\u308b\u6982\u5ff5\u3002\u5927\u5b663, 4\u5e74\u3067\u306f\u3001\u5e7e\u4f55\u5f62\u72b6\u3092\u8abf\u3079\u308b\u9053\u5177\u3068\u3057\u3066\u5c0e\u5165\u3055\u308c\u308b\u3002\u8abf\u3079\u305f\u3044\u7a7a\u9593\u3092\u5206\u5272\u3057\u3001\u5404\u30d1\u30fc\u30c4\u306e\u5883\u754c\u306b\u3088\u308b\u95a2\u4fc2\u6027\u3092\u6570\u5b66\u7684\u306b\u66f8\u304d\u4e0a\u3052\u308b\u3053\u3068\u3067(\u305f\u3068\u3048\u60f3\u50cf\u304c\u96e3\u3057\u3044\u3082\u306e\u3067\u3082)\u5e7e\u4f55\u5f62\u72b6\u306e\u7279\u5fb4\u3092\u6349\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5c02\u9580\u7528\u8a9e\u3067\u306f\u300c\u95a2\u624b\u300d\u3068\u547c\u3070\u308c\u308b\u7a7a\u9593\u540c\u58eb\u306e\u7d44\u7e54\u7684\u306a\u5bfe\u5fdc\u3065\u3051\u306e\u9053\u5177\u306b\u3082\u306a\u3063\u3066\u3044\u308b\u3002  [\/mfn]  \u306f\u30b3\u30f3\u30c4\u30a7\u30d3\u30c3\u30c1(Kontsevich)  \u306e\u666e\u904d\u7a4d\u5206 [mfn]  \u30d0\u30b7\u30ea\u30a8\u30d5\u4e0d\u5909\u91cf\u3092\u3072\u3068\u307e\u3068\u3081\u306b\u8868\u3057\u305f\u3082\u306e\u306b\u76f8\u5f53\u3059\u308b\u7a4d\u5206\u3092\u3044\u3046\u3002\u3053\u3053\u306b\u3082\u7279\u7570\u7d50\u3073\u76ee\u304c\u6e80\u305f\u3059FI\u95a2\u4fc2\u5f0f\u304c\u73fe\u308c\u308b\u3002\u30b3\u30f3\u30c4\u30a7\u30d3\u30c3\u30c1\u306f1994\u5e74\u306e\u30d5\u30a3\u30fc\u30eb\u30ba\u8cde\u53d7\u8cde\u8005\u3002\u306a\u304a\u3001\u672c\u8ad6\u6587\u3067\u306f\u570f\u8ad6\u5316\u3057\u305fFI\u95a2\u4fc2\u5f0f\u3092\u4e16\u754c\u3067\u521d\u3081\u3066\u8a18\u8ff0\u3057\u305f\u3002  [\/mfn] \u306b\u73fe\u308c\u308bFI \u95a2\u4fc2\u5f0f\u3092\u6e80\u305f\u3057\u3001\u975e\u81ea\u660e\u3067\u3042\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u69cb\u6210\u7269\u304b\u3089\u30b8\u30e7\u30fc\u30f3\u30ba\u591a\u9805\u5f0f\u306e\u60c5\u5831\u306f\u5168\u3066\u56de\u5fa9\u3057\u307e\u3059\u3002\u306a\u304a\u3001\u4f0a\u85e4\u306e\u8abf\u3079\u305f\u9650\u308a\u3067\u306f\u3001\u3053\u306e\u3088\u3046\u306a\u5fae\u5206\u306e\u6b21\u6570\u3082\u5fdc\u7528\u3067\u304d\u308b\u3088\u3046\u306a\u3001\u7279\u7570\u7d50\u3073\u76ee\u3078\u62e1\u5f35\u304c\u306a\u3055\u308c\u305f\u30db\u30d0\u30ce\u30d5\u30db\u30e2\u30ed\u30b8\u30fc\u306f\u521d\u3081\u3066\u3068\u306a\u308a\u307e\u3059\u3002<br>\u3000\u4ee5\u4e0a\u304b\u3089\u7d50\u3073\u76ee\u3092 \u8abf\u3079\u308b\u3053\u3068\u306b\u7528\u3044\u3089\u308c\u3066\u304d\u305f20\u4e16\u7d00\u7684\u306a\u300c\u5fae\u5206\u300d\u306f\u3001\u300c\u7d10\u306e\u4ea4\u5dee\u4ea4\u63db\u300d\u306b\u304a\u3051\u308b\u30db\u30e2\u30ed\u30b8\u30fc\u5b8c\u5168\u7cfb\u5217 [mfn]   \u30db\u30e2\u30ed\u30b8\u30fc\u306f\u6b21\u6570\u3068\u3044\u3046\u6574\u6570\u3092\u6301\u3061\u3001\u5e7e\u4f55\u5b66\u7684\u306a\u7a7a\u9593\u5f62\u72b6\u3092\u3088\u308a\u5206\u6790\u7684\u306b\u6349\u3048\u3089\u308c\u308b\u3002\u8abf\u67fb\u3057\u305f\u3044\u7a7a\u9593\u304c\u3001\u3055\u3089\u306b\u5225\u306e\uff12\u3064\u7a7a\u9593\u5bfe\u3068\u306e\u95a2\u4fc2\u6027\u306b\u3088\u308a\u3001\u5206\u6790\u3067\u304d\u308b\u5834\u5408\u3001\uff13\u3064\u7d44\u306e\u7a7a\u9593\u5bfe\u3092\u5ff5\u982d\u306b\u304a\u3044\u3066\u3001\u30db\u30e2\u30ed\u30b8\u30fc\u5b8c\u5168\u5217\u3068\u3044\u3046\u3001\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306e\u5217\u304c\u5b58\u5728\u3057\u3001\u79c1\u305f\u3061\u306b\u8c4a\u304b\u306a\u7a7a\u9593\u60c5\u5831\u3092\u63d0\u4f9b\u3059\u308b\u3002\u672c\u8ad6\u6587\u3067\u306f\u65b0\u3057\u3044\u30db\u30e2\u30ed\u30b8\u30fc\u5b8c\u5168(\u7cfb)\u5217\u3092\u4e16\u306e\u4e2d\u306b\u4e0e\u3048\u305f\u3002 [\/mfn] \u3060\u3068\u3044\u3046\u3053\u3068\u304c\u4eca\u56de\u6570\u5b66\u306b\u3088\u3063\u3066\u521d\u3081\u3066\u63a2\u3057\u5f53\u3066\u3089\u308c\u3001\u8a3c\u660e\u3055\u308c\u305f\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">\u3010\u5fdc\u7528\u4e0a\u306e\u30dd\u30a4\u30f3\u30c8\u3011<br> (1) \u767a\u898b\u3055\u308c\u305f\u30db\u30e2\u30ed\u30b8\u30fc\u306f\u4eca\u307e\u3067\u306b\u306a\u3044\u6027\u8cea\u3092\u6301\u3064\u3053\u3068\u304c\u6570\u5b66\u3067\u8a3c\u660e\u3055\u308c\u305f\u3002 <br> (2) \u7269\u7406\u5b66\u306b\u304a\u3051\u308b\u5834\u306e\u7406\u8ad6\u3001\u91cf\u5b50\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3001\u5316\u5b66\u3001\u751f\u7269\u5b66\u3078\u306e\u5fdc\u7528\u304c\u671f\u5f85\u3055\u308c\u308b\u3002 <\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/8fd022266db17de0e5bc26fc08e09b9b-1024x959.png\" alt=\"\" class=\"wp-image-24042\" width=\"512\" height=\"480\"\/><figcaption>\u4f0a\u85e4\u3000\u6607\u6c0f<br>\u300c\u5199\u771f\u63d0\u4f9b\uff1a\u6570\u5b66\u30bb\u30df\u30ca\u30fc\u7de8\u96c6\u90e8\u300d<\/figcaption><\/figure><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"has-medium-font-size wp-block-paragraph\"> \u3010\u7814\u7a76\u8cbb\u3078\u306e\u30b3\u30e1\u30f3\u30c8\uff08\u4ee3\u8868\u8005\u3000\u4f0a\u85e4\u6607\uff09\u3011<br> \u3053\u306e\u6625\u3001\u79d1\u5b66\u6280\u8853\u7814\u7a76\u8cbb\u88dc\u52a9\u91d1\uff08\u7814\u7a76\u8ab2\u984c\u756a\u53f720K03604\uff09\u306b\u3088\u308b\u7814\u7a76\u3082\u30b9\u30bf\u30fc\u30c8\u3057\u307e\u3057\u305f\u3002 <br> \u7814\u7a76\u8ab2\u984c\u540d\uff1a\u300c\u30d0\u30b7\u30ea\u30a8\u30d5\u4e0d\u5909\u91cf\u306e\u570f\u8ad6\u5316\u306e\u63a2\u6c42\u3068\u5c55\u958b\u300d\u3001 <br> \u7814\u7a76\u4ee3\u8868\u8005\uff1a\u4f0a\u85e4\u6607\uff08\u8328\u57ce\u9ad8\u5c02\uff09\u3001\u7814\u7a76\u5206\u62c5\u8005\uff1a\u521d\u7530\u771f\u77e5\u5b50\uff08\u9806\u5929\u5802\u5927\u5b66\uff09\u3001\u5409\u7530\u7d14\uff08\u6771\u4eac\u5927\u5b66\uff09\u3002 <br> \u3053\u306e\u7814\u7a76\u3092\u5f37\u529b\u306b\u63a8\u9032\u3057\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3063\u3066\u3044\u307e\u3059\u3002  <\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> \u3010\u5171\u8457\u8005\uff1a\u5409\u7530\u7d14\u6c0f\uff08\u6771\u4eac\u5927\u5b66\uff09\u306e\u30b3\u30e1\u30f3\u30c8\u3011 <\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<div style=\"border: 5px solid #87cefa; padding: 10px; border-radius: 0px; background: ##ffffff;\"><span style=\"font-size: large;\">Vassiliev \u306e\u7406\u8ad6\u306f\u3001\u3082\u3068\u3082\u3068\u7d50\u3073\u76ee\u5168\u4f53\u306e\u6210\u3059\u7121\u9650\u6b21\u5143\u7a7a\u9593\u306e\u89e3\u6790\u304b\u3089\u5f97\u3089\u308c\u305f\u3082\u306e\u3067\u3059\u304c\u3001\u3053\u306e\u3088\u3046\u306a\u9ad8\u6b21\u5143\u7684\u306a\u7406\u8ad6\u306e\u80cc\u666f\u306b\u306f\u3001\u570f\u8ad6\u7684\u8996\u70b9\u304c\u81ea\u7136\u306b\u73fe\u308f\u308c\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u3001\u672c\u7814\u7a76\u306b\u304a\u3044\u3066\u3082\u3053\u306e\u9ad8\u6b21\u5143\u3068\u570f\u8ad6\u3068\u306e\u5bfe\u5fdc\u306f\u89b3\u6e2c\u3055\u308c\u3066\u304a\u308a\u3001\u4f8b\u3048\u3070\u4ea4\u5dee\u4ea4\u63db\u306e\u4e0d\u5909\u6027\u3084 FI \u95a2\u4fc2\u5f0f\u306e\u4e2d\u306b\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u5ef6\u9577\u3068\u3057\u3066\u3001\u3055\u3089\u306b\u9ad8\u6b21\u306e\u95a2\u4fc2\u5f0f\u304c\u570f\u8ad6\u7684\u306b\u6349\u3048\u3089\u308c\u308b\u306f\u305a\u3067\u3001\u7d50\u3073\u76ee\u3092\u3088\u308a\u65b0\u3057\u3044\u5305\u62ec\u7684\u306a\u8996\u70b9\u304b\u3089\u7406\u89e3\u3067\u304d\u308b\u3068\u671f\u5f85\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/eab5ab7adcddcf630aea8bdd153153a4-1024x684.png\" alt=\"\" class=\"wp-image-24043\" width=\"357\" height=\"239\"\/><figcaption>\u5409\u7530\u3000\u7d14\u6c0f<br>\u300c\u5199\u771f\u63d0\u4f9b\uff1aCT2017\u300d<\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">\u3010\u672c\u8ad6\u6587\u306e\u554f\u984c\u3092\u89e3\u3044\u305f\u6642\u306e\u9ed2\u677f\u5199\u771f\u3011<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/info\/wp-content\/uploads0\/2020\/06\/c9bf449e2f032fd570a7fbe10ce15e4f-1024x768.png\" alt=\"\" class=\"wp-image-24036\" width=\"1024\" height=\"768\"\/><\/figure>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">&lt;\u30d7\u30ec\u30ea\u30ea\u30fc\u30b9\u82f1\u8a9e\u8981\u7d04&gt;<br> In this paper, we obtain a categorified version of Vassiliev skein relation on Khovanov homology. More precisely, we show that a genus-one operation on TQFT gives rise to a crossing change on Khovanov complexes. The invariance under Reidemeister moves turns out, and it enables us to extend Khovanov homology to singular links. We then see that its long exact sequence categorifies Vassiliev skein relation for the Jones polynomials. We also obtain the categorified FI relation. <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> \u3010\u8ad6\u6587\u60c5\u5831\u3011 <br> \u2605\u8ad6\u6587\u30bf\u30a4\u30c8\u30eb\uff1aCrossing change on Khovanov homology and a categorified Vassiliev skein relation (arXiv:1911.09308, with Jun Yoshida) <br> URL: <a href=\"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218216520500510\">https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218216520500510<\/a><br><br> \u2605\u30b8\u30e3\u30fc\u30ca\u30eb\u540d\uff1aJournal of Knot Theory and Its Ramifications <br> URL\uff1a <a href=\"https:\/\/www.worldscientific.com\/worldscinet\/jktr\">https:\/\/www.worldscientific.com\/worldscinet\/jktr<\/a><br> \u8457\u8005\uff1a\u4f0a\u85e4 \u6607, \u5409\u7530 \u7d14 <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> \u3010\u53c2\u8003\u6587\u732e\u60c5\u5831\u3011 <br> Noboru Ito, \u201cChain homotopy maps for Khovanov homology\u201d, Journal of Knot Theory and Its Ramifications, 2011, 20(1), pp127-139. <br><br> \u6df1\u8c37\u8ce2\u6cbb\uff0c\u30b2\u30fc\u30b8\u7406\u8ad6\u3068\u30b7\u30f3\u30d7\u30ec\u30c3\u30af\u30c6\u30a3\u30c3\u30af\u5e7e\u4f55\u5b66\u306b\u304a\u3051\u308b\u4e0d\u5909\u91cf\u306e\u30ab\u30c6\u30b4\u30ea\u30fc\u5316\u306b\u3064\u3044\u3066\uff0c\u7b2c17\u56de\u9ad8\u6728\u30ec\u30af\u30c1\u30e3\u30fc\u62db\u5f85\u8b1b\u6f14\uff082016\u5e746\u6708\uff09\uff0c\u4eac\u90fd\u5927\u5b66\uff0c\u30aa\u30f3\u30e9\u30a4\u30f3URL\uff1a<a href=\"https:\/\/www.ms.u-tokyo.ac.jp\/~toshi\/jjm\/JJMJ\/JJM_JHP\/contents\/takagi_jp\/17th\/TL-Fukaya_jp.html\">https:\/\/www.ms.u-tokyo.ac.jp\/~toshi\/jjm\/JJMJ\/JJM_JHP\/contents\/takagi_jp\/17th\/TL-Fukaya_jp.html<\/a>\uff08\u53c2\u71672020\u5e745\u670819\u65e5\uff09 <br><br> \u65e5\u7d4c\u30b5\u30a4\u30a8\u30f3\u30b9\uff0c\u201c\u30c1\u30e3\u30fc\u30f3\u8cde\u3092\u67cf\u539f\u6b63\u6a39\u6c0f\u304c\u53d7\u8cde\u201d\uff0c\u65e5\u7d4c\u30b5\u30a4\u30a8\u30f3\u30b92018\u5e7410\u6708\u53f7\uff0c <a href=\"http:\/\/www.nikkei-science.com\/?p=57088\">http:\/\/www.nikkei-science.com\/?p=57088<\/a>\uff0c\uff08\u53c2\u71672020\u5e745\u670819\u65e5\uff09 <br><br> \u4e80\u5c71\u660c\u4e5f\uff0c\u300cLMOV \u4e88\u60f3\u3068\u305d\u306e\u7cbe\u5bc6\u5316\u300d\uff0c\u7814\u7a76\u96c6\u4f1a\u300c\u7d50\u3073\u76ee\u306e\u6570\u5b66X\u300d\u5831\u544a\u96c6(2017), \u30aa\u30f3\u30e9\u30a4\u30f3URL: <a href=\"http:\/\/www.math.twcu.ac.jp\/mok10\/proc\/15Kameyama.pdf\">http:\/\/www.math.twcu.ac.jp\/mok10\/proc\/15Kameyama.pdf<\/a>\u3000,\uff08\u53c2\u71672020\u5e745\u670819\u65e5\uff09 <br><br> CT2017(International Category Theory Conference 2017)(2017\u5e747\u6708), Canada,\u3000\u30aa\u30f3\u30e9\u30a4\u30f3URL\uff1a <a href=\"http:\/\/www.mat.uc.pt\/~ct2017\/\">http:\/\/www.mat.uc.pt\/~ct2017\/<\/a>\u3000\uff0c\uff08\u53c2\u71672020\u5e745\u670819\u65e5\uff09 <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> <br>\u3010\u672c\u4ef6\u306b\u95a2\u3059\u308b\u554f\u3044\u5408\u308f\u305b\u5148\u3011 <br> \u8328\u57ce\u5de5\u696d\u9ad8\u7b49\u5c02\u9580\u5b66\u6821 \u56fd\u969b\u5275\u9020\u5de5\u5b66\u79d1 \u4e00\u822c\u6559\u990a\u90e8\u3000\u8b1b\u5e2b <br> \u4f0a\u85e4\u3000\u6607\uff08\u3044\u3068\u3046\u3000\u306e\u307c\u308b\uff09 <br> Tel: 029-272-5201\/029-271-2614\uff08\u7814\u7a76\u5ba4\u76f4\u901a\uff09 <br> E-mail: nito\u2605ibaraki-ct.ac.jp\uff08\u2605\u3092\uff20\u306b\u5909\u63db\u9858\u3044\u307e\u3059\u3002\uff09 <\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"> <br>\uff08\u5831\u9053\u306b\u3064\u3044\u3066\uff09 <br> \u8328\u57ce\u5de5\u696d\u9ad8\u7b49\u5c02\u9580\u5b66\u6821 \u7dcf\u52d9\u8ab2 \u7814\u7a76\u5354\u529b\uff65\u5730\u57df\u9023\u643a\u4fc2 <br> Tel: 029-271-2952 <br>E-mail:kenkyo\u2605sec.ibaraki-ct.ac.jp\uff08\u2605\u3092\uff20\u306b\u5909\u63db\u9858\u3044\u307e\u3059\u3002\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65b0\u305f\u306a\u7d50\u3073\u76ee\u7406\u8ad6\u3067\u300c\u5fae\u5206\u300d\u306e\u6982\u5ff5\u3092\u5237\u65b0 \u2014\u570f\u8ad6\u5316\u306b\u3088\u308b\u7d50\u3073\u76ee\u30db\u30e2\u30ed\u30b8\u30fc\u3067\u91cf\u5b50\u8ad6\u3078\u306e\u66f4\u306a\u308b\u5fdc\u7528\u304c\u671f\u5f85\u2014 [&hellip;]<\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,9],"tags":[70],"class_list":["post-24436","post","type-post","status-publish","format-standard","hentry","category-about","category-department","tag-70"],"_links":{"self":[{"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/posts\/24436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/comments?post=24436"}],"version-history":[{"count":1,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/posts\/24436\/revisions"}],"predecessor-version":[{"id":64535,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/posts\/24436\/revisions\/64535"}],"wp:attachment":[{"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/media?parent=24436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/categories?post=24436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ibaraki-ct.ac.jp\/info\/wp-json\/wp\/v2\/tags?post=24436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}