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1990\u5e74\u3001\u5f7c\u306f\u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u306b\u3042\u308b\u65b0\u3057\u304f\u8a2d\u7acb\u3055\u308c\u305f\u30a2\u30a4\u30b6\u30c3\u30af\u30cb\u30e5\u30fc\u30c8\u30f3\u6570\u5b66\u7814\u7a76\u6240\u306e\u30c7\u30a3\u30ec\u30af\u30bf\u30fc\u3068\u540c\u6642\u306b\u3001\u30c8\u30ea\u30cb\u30c6\u30a3\u30ab\u30ec\u30c3\u30b8\u306e\u300c\u30de\u30b9\u30bf\u30fc\u300d\u306b\u306a\u308a\u307e\u3057\u305f\u3002 1955\u5e74\u3001\u5f7c\u306f\u6570\u5b66\u8005\u306e\u30ea\u30ea\u30fc\u30fb\u30d6\u30e9\u30a6\u30f3\uff081928\u20132018\uff09\u3068\u7d50\u5a5a\u3057\u30013\u4eba\u306e\u606f\u5b50\u304c\u3044\u307e\u3057\u305f\u3002\u5f7c\u5973\u306f\u30e1\u30a2\u30ea\u30fc\u30fb\u30ab\u30fc\u30c8\u30e9\u30a4\u30c8\u304b\u3089\u535a\u58eb\u53f7\u3092\u53d6\u5f97\u3057\u3001\u6570\u5b66\u7684\u306a\u30ad\u30e3\u30ea\u30a2\u3092\u3042\u304d\u3089\u3081\u308b\u524d\u306b\u30d9\u30c3\u30c9\u30d5\u30a9\u30fc\u30c9\u5927\u5b66\u306e\u8b1b\u5e2b\u3067\u3057\u305f\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Atiyah\u306f\u5f53\u521d\u3001Hodge\u306e\u5b66\u751f\u3068\u3057\u3066\u4ee3\u6570\u5e7e\u4f55\u5b66\u3092\u6271\u3063\u3066\u3044\u307e\u3057\u305f\u3002 1954\u5e74\u3001\u5f7c\u306f\u901a\u5e38\u306e\u5730\u57df\u306e\u8abf\u7406\u7406\u8ad6\u7684\u6271\u3044\u3067\u50cd\u3044\u305f\u3053\u3068\u3067\u30b9\u30df\u30b9\u8cde\u3092\u53d7\u8cde\u3057\u307e\u3057\u305f\u3002\u5f7c\u306e\u8ad6\u6587\u306f\u3001\u7a4d\u5206\u306e\u6599\u7406\u7406\u8ad6\u3092\u6271\u3063\u305f2.\u30bd\u30ed\u30e2\u30f3\u30fb\u30ec\u30d5\u30b7\u30a7\u30c3\u30c4\u306e\u4ee3\u6570\u54c1\u7a2e\u306b\u95a2\u3059\u308b\u82b8\u8853\u3002  Atiyah\u3068Friedrich Hirzebruch 1977 1960\u5e74\u4ee3\u3001\u5f7c\u306f\u30c8\u30dd\u30ed\u30b8\u30fcK\u7406\u8ad6\u306e\u5275\u8a2d\u8005\u306e\u4e00\u4eba\u3067\u3042\u308a\u3001\u30d9\u30af\u30bf\u30fc\u30d0\u30f3\u30c9\u30eb\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u5171\u540c\u7406\u8ad6\u3067\u3059\u3002\u3053\u306e\u63d0\u6848\u306f\u3001\u30a2\u30ec\u30af\u30b5\u30f3\u30c0\u30fc\u30fb\u30b0\u30ed\u30c6\u30f3\u30c7\u30a3\u30a8\u30c3\u30af\u306b\u3088\u308b\u30ea\u30fc\u30de\u30f3\u30fb\u30ed\u30c3\u30af\u306e\u6587\u306e\u4e00\u822c\u5316\u3068\u3001\u30e9\u30a6\u30eb\u30fb\u30dc\u30c3\u30c8\u304c\u8a2d\u5b9a\u3057\u305f\u5468\u671f\u6027\u304b\u3089\u6765\u307e\u3057\u305f\u3002 Atiyah\u306f\u3001\u305f\u3068\u3048\u3070\u3001\u30c8\u30dd\u30ed\u30b8\u30fcK\u7406\u8ad6\u3092\u4f7f\u7528\u3057\u3066\u3001John Frank Adams\u306b\u3088\u308bHopf-Invariant 1\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u8907\u96d1\u306a\u89e3\u6c7a\u7b56\u3092\u7c21\u7d20\u5316\u3057\u3001\u305d\u306e\u4ed6\u306e\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u554f\u984c\u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002 1963\u5e74\u3001\u30a4\u30b5\u30c9\u30fc\u30ebM.\u30b7\u30f3\u30ac\u30fc\u3068\u3068\u3082\u306b\u3001\u5f7c\u306f\u30a2\u30c6\u30a3\u30e4\u30b7\u30f3\u30ac\u30fc\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30bb\u30c3\u30c8\u3092\u5b9f\u8a3c\u3057\u307e\u3057\u305f\u3002 [2] \u3053\u308c\u306f\u300120\u4e16\u7d00\u306e\u6700\u3082\u91cd\u8981\u306a\u6570\u5b66\u7684\u6587\u306e1\u3064\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u6587\u306f\u3001M\u306e\u30c8\u30dd\u30ed\u30b8\u30fc\u30a4\u30f3\u30de\u30a4\u30a2\u30f3\u30c8\u306b\u3088\u308b\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30de\u30cb\u30db\u30fc\u30eb\u30c9M\u3067\u3001\u6955\u5186\u5f62\u306e\u7dda\u5f62\u5fae\u5206\u6f14\u7b97\u5b50\uff08Laplace\u6f14\u7b97\u5b50\u3001DIRAC\u6f14\u7b97\u5b50\u306a\u3069\uff09\u306e\u5206\u6790\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u62bc\u3057\u307e\u3059\uff08\u30aa\u30a4\u30e9\u30fc\u30dd\u30a4\u30f3\u30ab\u30ec\u306e\u7279\u6027\u3092\u901a\u3057\u3066\u6700\u3082\u5358\u7d14\u306a\u30b1\u30fc\u30b9\u3067\u306f\u3001\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u306e\u30bf\u30a4\u30d7\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\uff09\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5206\u6790\u3068\u30c8\u30dd\u30ed\u30b8\u30fc\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u73fe\u4ee3\u306e\u7269\u7406\u5b66\u306b\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u5fae\u5206\u6f14\u7b97\u5b50\u306e\u300c\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306f\u3001\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u30d9\u30af\u30c8\u30eb\u30eb\u30fc\u30e0\u306e\u5bf8\u6cd5\u306e\u9055\u3044\u3068\u3001\u30a2\u30b8\u30e5\u30f3\u30b0\u3055\u308c\u305f\u6f14\u7b97\u5b50\u306e\u5bf8\u6cd5\u306e\u9055\u3044\u3067\u3059\u3002\u5f7c\u306f\u307e\u305f\u30011970\u5e74\u4ee3\u306b\u30b5\u30fc\u30de\u30eb\u30d1\u30a4\u30d7\u65b9\u7a0b\u5f0f\uff08\u62e1\u6563\u65b9\u7a0b\u5f0f\uff09\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u3053\u306e\u6587\u306e\u65b0\u3057\u3044\u3088\u308a\u5358\u7d14\u306a\u8a3c\u62e0\u306b\u53c2\u52a0\u3057\u307e\u3057\u305f\uff08Raoul Bott\u3001Patodi 1973\uff09\u3002\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u6587\u306b\u306f\u3001\u4ee3\u6570\u5e7e\u4f55\u5b66\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3082\u3042\u308a\u307e\u3059\u3002\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3068\u3057\u3066Riemann-Roch\u306e\u6587\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u6570\u5b66\u306eDIRAC\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3067\u3042\u308bAtiyah\u3068\u6b4c\u624b\u3092\u300c\u767a\u898b\u3057\u305f\u300dAtiyah\u3068\u300c\u767a\u898b\u300d\u306b\u95a2\u9023\u3057\u3066\u3002\u6709\u540d\u306a\u6587\u306e\u52d5\u6a5f\u306f\u30a4\u30b9\u30e9\u30a8\u30eb\u30fb\u30b2\u30eb\u30d5\u30a1\u30f3\u30c9\u304b\u3089\u6765\u307e\u3057\u305f\uff08 \u6955\u5186\u65b9\u7a0b\u5f0f\u306b\u3064\u3044\u3066 \u3001\u30e9\u30b9\u3002\u7b97\u6570\u3002\u8abf\u67fb1960\uff09\u3002 \u30e9\u30a6\u30eb\u30fb\u30dc\u30c3\u30c8\u3068\u3068\u3082\u306b\u3001\u5f7c\u306f\u30ec\u30d5\u30b7\u30a7\u30c3\u30c4\u306e\u56fa\u5b9a\u70b9\u306e\u4e00\u822c\u5316\u3067\u3042\u308b\u30a2\u30c6\u30a3\u30e4\u30fb\u30dc\u30c3\u30c8\u306e\u56fa\u5b9a\u5211\u3092\u793a\u3057\u307e\u3057\u305f\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30a2\u30c6\u30a3\u30e4\u306f\u3001\u6570\u5341\u5e74\u306b\u308f\u305f\u3063\u3066\u6570\u5b66\u3068\u7269\u7406\u5b66\u306e\u9593\u3067\u305f\u3086\u307e\u306c\u4ef2\u4ecb\u3092\u7372\u5f97\u3057\u3066\u304d\u307e\u3057\u305f\u3002\u7279\u306b\u3001\u5f7c\u306f\u3001\u591a\u69d8\u6027\u306e\u975e\u7dda\u5f62\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u3042\u308b\u5b89\u5b9a\u3057\u306a\u3044\u30aa\u30fc\u30af\u7406\u8ad6\uff08\u30e4\u30f3\u30df\u30eb\u30ba\u7406\u8ad6\uff09\u306b\u8208\u5473\u304c\u3042\u308a\u307e\u3057\u305f\u3002\u81ea\u5df1\u4e8c\u5143\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30e4\u30f3\u30df\u30eb\u30ba\u7406\u8ad6\u306b\u304a\u3051\u308b\u30a4\u30f3\u30b9\u30bf\u30f3\u30c8\u30f3\u306eADHM\u69cb\u9020\u306f\u3001\u5f7c\u3068\u30ca\u30a4\u30b8\u30a7\u30eb\u30d2\u30c3\u30c1\u30f3\u3001\u30a6\u30e9\u30b8\u30df\u30fc\u30eb\u30c9\u30ea\u30f3\u30d5\u30a7\u30eb\u30c9\u3001\u30e6\u30fc\u30ea\u30de\u30cb\u30f3\u304b\u3089\u6765\u3066\u3044\u307e\u3059\u3002 [3] \u3057\u304b\u3057\u3001\u6570\u5b66\u3067\u30a8\u30c9\u30ef\u30fc\u30c9\u30fb\u30a6\u30a3\u30c3\u30c6\u30f3\u306b\u3088\u3063\u3066\u5c0e\u5165\u3055\u308c\u305f\u91cf\u5b50\u7551\u306e\u7406\u8ad6\u7684\u624b\u6cd5\uff08\u65b0\u3057\u3044\u30ce\u30fc\u30c9\u306e\u4e0d\u5909\u5264\u304b\u3089\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u307e\u3067 [4] \u5f7c\u306f\u30b9\u30fc\u30d1\u30fc\u4ea4\u97ff\u66f2\u3068\u6587\u5b57\u5217\u7406\u8ad6\u306b\u5230\u9054\u3057\u307e\u3057\u305f\uff09\u3002 Atiyah\u306e\u591a\u304f\u306e\u30a2\u30a4\u30c7\u30a2\u306f\u30011980\u5e74\u4ee3\u304b\u3089\u7269\u7406\u5b66\u8005\u306b\u3088\u3063\u3066\u53d6\u308a\u4e0a\u3052\u3089\u308c\uff08\u8d85\u5bfe\u79f0\u6027\u306e\u3042\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u6587\u306e\u65b0\u3057\u3044\u8a3c\u62e0\u3092\u542b\u3080\uff09\u3001\u3055\u3089\u306b\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002 \u3053\u308c\u306f\u3001Isaac Newton Institute\u306e\u57fa\u790e\u306e\u80cc\u5f8c\u306b\u3042\u308b\u539f\u52d5\u529b\u3067\u3042\u308a\u3001\u30a4\u30f3\u30bf\u30fc\u30a2\u30ab\u30c7\u30df\u30fc\u30d1\u30cd\u30eb\uff08IAP\uff09\u3001\u6b27\u5dde\u30a2\u30ab\u30c7\u30df\u30fc\u5354\u4f1a\uff08ALLEA\uff09\u3001\u304a\u3088\u3073\u6b27\u5dde\u6570\u5b66\u5354\u4f1a\u306e\u5f62\u6210\u306b\u304a\u3044\u3066\u969b\u306e\u539f\u52d5\u529b\u3067\u3057\u305f\u3002 [5] \u5f7c\u306e\u5b66\u751f\u306b\u306f\u3001\u30b5\u30a4\u30e2\u30f3\u30fb\u30c9\u30ca\u30eb\u30c9\u30bd\u30f3\u3001\u30ca\u30a4\u30b8\u30a7\u30eb\u30fb\u30d2\u30c3\u30c1\u30f3\u3001\u30d4\u30fc\u30bf\u30fc\u30fb\u30af\u30ed\u30f3\u30cf\u30a4\u30de\u30fc\u3001\u30b0\u30ec\u30fc\u30e0\u30fb\u30b7\u30fc\u30ac\u30eb\u3001\u30d5\u30e9\u30f3\u30b7\u30b9\u30fb\u30ad\u30eb\u30ef\u30f3\u3001\u30eb\u30fc\u30b9\u30fb\u30ed\u30fc\u30ec\u30f3\u30b9\u304c\u542b\u307e\u308c\u307e\u3059\u3002 1974\u5e74\u304b\u30891976\u5e74\u307e\u3067\u3001\u5f7c\u306f\u30ed\u30f3\u30c9\u30f3\u6570\u5b66\u5354\u4f1a\u306e\u4f1a\u9577\u3067\u3042\u308a\u30011990\u5e74\u304b\u30891995\u5e74\u307e\u3067\u738b\u7acb\u5354\u4f1a\u4f1a\u9577\u3067\u3057\u305f\u3002\u5f7c\u306f\u307e\u305f\u3001\u30a8\u30c7\u30a3\u30f3\u30d0\u30e9\u738b\u7acb\u5354\u4f1a\u306e\u4f1a\u9577\u3067\u3042\u308a\u3001\u305d\u306e\u4ef2\u9593\u3067\u3057\u305f\u3002\u5f7c\u306f\u3001\u30a2\u30ab\u30c7\u30df\u30fc\u30fb\u30c7\u30fb\u30b5\u30a4\u30a8\u30f3\u30b9\u3001\u30ed\u30b7\u30a2\u8a9e\u3001\u30a6\u30af\u30e9\u30a4\u30ca\u8a9e\u3001\u30ce\u30eb\u30a6\u30a7\u30fc\u8a9e\u3001\u30b9\u30da\u30a4\u30f3\u8a9e\u3001\u30b9\u30a6\u30a7\u30fc\u30c7\u30f3\u8a9e\u3001\u30a2\u30a4\u30eb\u30e9\u30f3\u30c9\u3001\u30aa\u30fc\u30b9\u30c8\u30e9\u30ea\u30a2\u79d1\u5b66\u30a2\u30ab\u30c7\u30df\u30fc\u306a\u3069\u3001\u591a\u304f\u306e\u30a2\u30ab\u30c7\u30df\u30fc\u306e\u5916\u56fd\u4eba\u30e1\u30f3\u30d0\u30fc\u3067\u3057\u305f\u3002\u5f7c\u306f\u307e\u305f\u3001\u591a\u304f\u306e\u540d\u8a89\u6587\u66f8\u3092\u53d7\u3051\u53d6\u308a\u307e\u3057\u305f\u3002 1997\u5e74\u304b\u30892002\u5e74\u307e\u3067\u3001\u5f7c\u306f\u79d1\u5b66\u3068\u4e16\u754c\u60c5\u52e2\u306b\u95a2\u3059\u308bPugwash Conferences\u306e\u4f1a\u9577\u3067\u3057\u305f\u3002 \u672c\uff1a\u672c\uff1a \u30a4\u30a2\u30f3G.\u30de\u30af\u30c9\u30ca\u30eb\u30c9\u3068\uff1a \u901a\u52e4\u4ee3\u6570\u306e\u7d39\u4ecb\u3002 Addison-Wesley 1969 \u6955\u5186\u5f62\u306e\u30aa\u30da\u30ec\u30fc\u30bf\u30fc\u3068\u30b3\u30f3\u30d1\u30af\u30c8\u30b0\u30eb\u30fc\u30d7\u3001 \u6570\u5b66401\u306e\u8b1b\u7fa9\u30ce\u30fc\u30c8\u3001Springer 1974 \uff08ed\u3002\u304a\u3088\u3073co -author\uff09 \u5618\u30b0\u30eb\u30fc\u30d7\u306e\u8868\u73fe\u7406\u8ad6\u3002 1977\u5e74 \u30e4\u30f3\u30df\u30eb\u30ba\u30d5\u30a3\u30fc\u30eb\u30c9\u306e\u30b8\u30aa\u30e1\u30c8\u30ea \u3001\u30d5\u30a7\u30eb\u30df\u30ec\u30af\u30c1\u30e3\u30fc\u3001Accademia dei lincei\u3001Pisa 1979 \u53ce\u96c6\u3055\u308c\u305f\u4f5c\u54c1\u3002 \u30af\u30e9\u30ec\u30f3\u30c9\u30f3\u30d7\u30ec\u30b9\u3001\u30aa\u30c3\u30af\u30b9\u30d5\u30a9\u30fc\u30c9\u30017\u5dfb\u30011988\u5e74\u304b\u30892014\u5e74 K\u7406\u8ad6\u3002 \u30d9\u30f3\u30b8\u30e3\u30df\u30f31967\u30011989 MIT Nigel Hitchin\uff1a \u78c1\u6c17\u30e2\u30ce\u30dd\u30fc\u30eb\u306e\u30b8\u30aa\u30e1\u30c8\u30ea\u3068\u30c0\u30a4\u30ca\u30df\u30af\u30b9 \u3001M\u3002B\u3002\u30dd\u30fc\u30bf\u30fc\u30ec\u30af\u30c1\u30e3\u30fc\u3001\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u5927\u5b66\u51fa\u7248\u5c40\u30011988\u5e74 \u7d50\u3073\u76ee\u306e\u30b8\u30aa\u30e1\u30c8\u30ea\u3068\u7269\u7406\u5b66\u3002 \u30b1\u30f3\u30d6\u30ea\u30c3\u30b81990 Daniel Iagolnitzer\uff08ed\u3002and Co -author\uff09\uff1a \u30d5\u30a3\u30fc\u30eb\u30ba\u30e1\u30c0\u30a4\u30ea\u30b9\u30c8\u306e\u8b1b\u7fa9\u3002 World Scientific 1997\u30012003\u30013rd Edition with Chitat Chong 2015 \u30a8\u30c3\u30bb\u30a4\uff1a MIT ISADORE M.\u30b7\u30f3\u30ac\u30fc\uff1a \u30b3\u30f3\u30d1\u30af\u30c8\u30de\u30cb\u30db\u30fc\u30eb\u30c9\u4e0a\u306e\u6955\u5186\u6f14\u7b97\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3002 Bull\u3002AMS1963\u306f\u3001\u6570\u5b66\u306e\u5e74\u4ee3\u8a18\u306e\u591a\u304f\u306e\u30a8\u30c3\u30bb\u30a4\u3067\u8a3c\u660e\u3057\u3001\u53ce\u96c6\u3055\u308c\u305f\u4f5c\u54c1\u306e\u7b2c3\u5dfb\u306b\u518d\u3073\u5370\u5237\u3055\u308c\u307e\u3057\u305f\u3002 Atiyah-Singer Index\u30bb\u30c3\u30c8\u306e\u6587\u732e\u60c5\u5831\u3082\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 \u30e9\u30a6\u30eb\u30dc\u30c3\u30c8\u3068\uff1a \u6955\u5186\u5f62\u306e\u5fae\u5206\u6f14\u7b97\u5b50\u306e\u305f\u3081\u306eLefschetz\u56fa\u5b9a\u70b9\u5f0f\u3001 \u30a2\u30e1\u30ea\u30ab\u6570\u5b66\u5354\u4f1a\u306e\u7d00\u8981\u3001\u30d0\u30f3\u30c972\u30011966\u3001S\u3002245\uff08atiyah-bott-fixpunktsatz\uff09 \u30c8\u30e0\u932f\u4f53 \u3001Proc\u3002\u30ed\u30f3\u30c9\u30f3\u6570\u5b66\u3002 Soc\u3002\u3001Serie 3\u3001Band 11\u30011961\u3001S\u3002291\u2013310 \u6570\u5b66\u306b\u304a\u3051\u308b\u4ee3\u6570\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u5f79\u5272 \u3001Journal of the London Mathematical Society\u3001Band 41\u30011966\u3001S\u300263\u201369 \u6570\u5b66\u306e\u5909\u5316\u3068\u9032\u6b69 \u3001Image of Science\u30011969\u3001Issue 4\u3001pp\u3002314\u2013323\u3001Reprint In\uff1aMichael Otte\uff08ed\u3002\uff09\u3001 \u6570\u5b66\u306b\u3064\u3044\u3066\u306e\u6570\u5b66\u8005\u3002\u79d1\u5b66\u3068\u516c\u8846 \u3001\u30d9\u30eb\u30ea\u30f3\u30fb\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af1974\u3001ISBN 978-3-540-06898-3\u3001 doi\uff1a10.1007\/978-3-642-80866-1_8 \u3002 \u30dc\u30c3\u30c8\u3068\u4e00\u7dd2\u306b\u3001\u30d1\u30c8\u30c7\u30a3\uff1a \u71b1\u65b9\u7a0b\u5f0f\u3068\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u5b9a\u7406\u306b\u3064\u3044\u3066 \u3001 \u767a\u660e\u3002 Math\u3002\u3001Band 19\u30011973\u3001S\u3002279\u2013330\u3001Errata Band 28\u30011975\u3001S\u3002277\u2013280 \u30ea\u30c1\u30e3\u30fc\u30c9\u30fbS\u30fb\u30ef\u30fc\u30c9\u3068\uff1a \u30a4\u30f3\u30b9\u30bf\u30f3\u30c8\u30f3\u3068\u4ee3\u6570\u5e7e\u4f55\u5b66 \u3001comm\u3002\u7b97\u6570\u3002 Phys\u3002\u3001Band 55\u30011977\u3001S\u3002117\u2013124\u3001 \u30d7\u30ed\u30b8\u30a7\u30af\u30c8Euclid \u30a6\u30a3\u30eb\u30d5\u30ea\u30fc\u30c9\u30b7\u30e5\u30df\u30c3\u30c8\u3068\uff1a \u534a\u5618\u5618\u30b0\u30eb\u30fc\u30d7\u5411\u3051\u306e\u96e2\u6563\u30b7\u30ea\u30fc\u30ba\u306e\u5e7e\u4f55\u5b66\u7684\u69cb\u9020 \u6570\u5b66\u306e\u8abf\u67fb\u7d50\u679c\u3001\u30d0\u30f3\u30c942\u30011977\u3001S\u30021-62\u3001\u30a8\u30e9\u30bf\u3001\u30d0\u30f3\u30c954\u30011979\u3001S\u3002189-192 MIT I.\u30b7\u30f3\u30ac\u30fc\u3001N\u3002\u30d2\u30c3\u30c1\u30f3\uff1a 4\u6b21\u5143\u306e\u30ea\u30fc\u30de\u30cb\u30a2\u5e7e\u4f55\u5b66\u306e\u81ea\u5df1\u4e8c\u6b21\u6027\u3001 Proc\u3002\u30ed\u30a4\u3002 Soc\u3002 A\u3001\u30d0\u30f3\u30c9362\u30011978\u3001S\u3002425\u2013461 \u30b8\u30aa\u30e1\u30c8\u30ea\u3068\u306f\u4f55\u3067\u3059\u304b\uff1f \uff08\u5927\u7d71\u9818\u6f14\u8aac\uff09\u3001\u6570\u5b66\u5b98\u5831\u3001\u30d0\u30f3\u30c966\u30011982\u3001S\u3002179\u2013182 \u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6 \u3001\u30d1\u30d6\u3002\u7b97\u6570\u3002 IHES\u3001\u30d0\u30f3\u30c968\u30011988\u3001S\u3002175\u2013186 \u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u3068\u4f4e\u6b21\u5143\u306e\u30b8\u30aa\u30e1\u30c8\u30ea\u3001 \u7406\u8ad6\u7269\u7406\u5b66\u306e\u9032\u6b69\u3001\u88dc\u8db3NR\u3002 102\u30011990\u3001S\u30021 \u30b8\u30aa\u30e1\u30c8\u30ea\u3068\u7269\u7406\u5b66 \u3001The Mathematical Gazette\u3001Band 80\u30011996\u3001S\u300278\u201382 \u30b0\u30ed\u30fc\u30d0\u30eb\u30b8\u30aa\u30e1\u30c8\u30ea \uff08Bakerian Lecture\uff09\u3001American Mathematical Monthly\u3001Band 111\u30012004\u3001S\u3002716\u2013723 \u82e5\u3044\u6570\u5b66\u8005\u3078\u306e\u30a2\u30c9\u30d0\u30a4\u30b9 \u3001Timothy Gowers\u3067\u306f\u3001Imre Leader\uff08hrsg\u3002\uff09\u3001June Barrow-Green\uff1a \u6570\u5b66\u306e\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u30b3\u30f3\u30d1\u30cb\u30aa\u30f3 \u3001\u30d7\u30ea\u30f3\u30b9\u30c8\u30f3\u5927\u5b66\u51fa\u7248\u5c402008\u3001S\u30021006\u20131010 \u30a8\u30c7\u30a3\u30f3\u30d0\u30e9\u5e7e\u4f55\u5b66\u3001\u5206\u6790\u3001\u304a\u3088\u3073\u7269\u7406\u5b66\u306b\u95a2\u3059\u308b\u8b1b\u7fa9 \u30012010\u3001 arxiv \u30de\u30a4\u30b1\u30eb\u30fbJ\u30fb\u30d0\u30fc\u30cb\u30fc\uff1a \u30de\u30a4\u30b1\u30eb\u30fbF\u30fb\u30a2\u30c6\u30a3\u30e4\uff081929\u20132019\uff09 \u3002\u306e\uff1a \u81ea\u7136 \u3002 \u30d0\u30f3\u30c9  566 \u30012019\u5e742\u67081\u65e5 S.  40 \u3001doi\uff1a 10.1038\/d41586-019-00358-9 \uff08 Nature.com [2019\u5e742\u67089\u65e5\u306b\u30a2\u30af\u30bb\u30b9]\uff09\u3002  S.-T. yau\uff08hrsg\u3002\uff09\uff1a \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7406\u8ad6\u306e\u5275\u8a2d\u8005\uff1aAtiyah\u3001Bott\u3001Hirzebruch\u3001Singer\u306e\u56de\u60f3 \u3001\u30a4\u30f3\u30bf\u30fc\u30ca\u30b7\u30e7\u30ca\u30eb\u30d7\u30ec\u30b9\u3001\u30b5\u30de\u30fc\u30d3\u30eb2003\u3001\u30a2\u30c6\u30a3\u30e4\u306e\u4f1d\u8a18\u3068 \u30aa\u30f3\u30e9\u30a4\u30f3\u3001\u6570\u5b66\u306e\u304a\u795d\u3044 \u2191  \u30de\u30a4\u30b1\u30eb\u30fb\u30d5\u30e9\u30f3\u30b7\u30b9\u30fb\u30a2\u30c6\u30a3\u30e4 IM Mathematics Genealogy Project\uff08Englisch\uff09 \u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\uff1aMathgenealogyproject\/Maintenance\/ID\u306e\u4f7f\u7528  \u2191  \u6559\u79d1\u66f8\u306e\u8868\u73fe\u306f\u3001\u4f8b\u3048\u3070\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 Peter Gilkey\uff1a\u201e\u4e0d\u5909\u7406\u8ad6\u3001\u71b1\u65b9\u7a0b\u5f0f\u3001Atiyah-Singer-Indextheorem\u300d\u3001\u30aa\u30f3\u30e9\u30a4\u30f3 –  \u3001 \u30e1\u30eb\u30ed\u30fc\u30ba\uff1a Atiyah-Patodi-Singer Index\u5b9a\u7406 \u3001\u30aa\u30f3\u30e9\u30a4\u30f3\u30d6\u30c3\u30af  \u2191  Atiyah\u3001Hitchin\u3001Drinfeld\u3001Manin\u3001Instantons\u306e\u5efa\u8a2d\u3001Phys\u3002\u30ec\u30c3\u30c8\u3002 A\u3001\u30d0\u30f3\u30c965\u30011978\u3001S\u3002185\u2013187  \u2191  Atiyah\uff1a\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u91cf\u5b50\u30d5\u30a3\u30fc\u30eb\u30c9\u7406\u8ad6\u3001IHES\u306e\u6570\u5b66\u7684\u51fa\u7248\u7269\u3002\u30d0\u30f3\u30c968\u30011988\u3001S\u3002175\u2013186  \u2191  \u30a2\u30c6\u30a3\u30e4\u3068\u6b4c\u624b\u306f\u30a2\u30d9\u30eb\u8cde\u3092\u53d7\u8cde\u3057\u307e\u3059 \u3001\u901a\u77e5AMS\u30012004\u5e746\u6708\/7\u6708\u3001S\u3002649\u2013650  \u2191  \u30a2\u30e1\u30ea\u30ab\u82b8\u8853\u79d1\u5b66\u30a2\u30ab\u30c7\u30df\u30fc\u3002\u30e1\u30f3\u30d0\u30fc\u306e\u672c \uff08 PDF \uff09\u3002 2016\u5e744\u670815\u65e5\u306b\u53d6\u5f97  \u2191  \u304b\u3089\u306e\u30e1\u30f3\u30d0\u30fc\u30a8\u30f3\u30c8\u30ea 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1936\u5e74\uff1a\u30e9\u30fc\u30b9\u30fb\u30f4\u30a1\u30ec\u30ea\u30a2\u30f3\u30fb\u30a2\u30fc\u30eb\u30d5\u30a9\u30fc\u30b9\u3001\u30b8\u30a7\u30b7\u30fc\u30fb\u30c0\u30b0\u30e9\u30b9|1950\u5e74\uff1a\u30ed\u30fc\u30e9\u30f3\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u3001\u30a2\u30c8\u30eb\u30fb\u30bb\u30eb\u30d0\u30fc\u30b0|1954\u5e74\uff1a\u30b3\u30f3\u30c0\u30a4\u30e9\u30fb\u30b3\u30cb\u30ab\u30eb\u3001\u30b8\u30e3\u30f3\u30fb\u30d4\u30a8\u30fc\u30eb\u30fb\u30bb\u30fc\u30eb|1958\u5e74\uff1a\u30af\u30e9\u30a6\u30b9\u30fb\u30d5\u30ea\u30fc\u30c9\u30ea\u30c3\u30d2\u30fb\u30ed\u30b9\u3001\u30eb\u30cd\u30fb\u30c8\u30e0|1962\u5e74\uff1a\u30e9\u30fc\u30b9\u30fb\u30d8\u30eb\u30de\u30f3\u30c0\u30fc\u3001\u30b8\u30e7\u30f3\u30fb\u30df\u30eb\u30ca\u30fc|1966\uff1a \u30de\u30a4\u30b1\u30eb\u30fb\u30a2\u30c6\u30a3\u30e4 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Drinfeld\u3001Vaughan F. Jones\u3001Shigefumi Mori\u3001Edward Witten |1994\u5e74\uff1a\u30b8\u30e3\u30f3\u30d6\u30eb\u30ac\u30a4\u30f3\u3001\u30d4\u30a8\u30fc\u30eb\u30eb\u30a4\u30e9\u30a4\u30aa\u30f3\u30ba\u30e9\u30a4\u30aa\u30f3\u30ba\u3001\u30b8\u30e3\u30f3 – \u30ad\u30ea\u30b9\u30c8\u30a8\u30e8\u30c3\u30b3\u30b9\u3001\u30a8\u30d5\u30a3\u30e0\u30bc\u30eb\u30e2\u30d5|1998\uff1a\u30ea\u30c1\u30e3\u30fc\u30c9\u30fb\u30dc\u30fc\u30c1\u30a7\u30c3\u30ba\u3001\u30c6\u30a3\u30e2\u30b7\u30fc\u30fb\u30b4\u30fc\u30ef\u30fc\u30ba\u3001\u30de\u30ad\u30b7\u30e0\u30fb\u30b3\u30f3\u30bc\u30a6\u30a3\u30c3\u30c1\u3001\u30ab\u30fc\u30c6\u30a3\u30b9\u30fb\u30de\u30af\u30de\u30ec\u30f3|2002\u5e74\uff1a\u30ed\u30fc\u30e9\u30f3\u30fb\u30e9\u30d5\u30a9\u30fc\u30b0\u3001\u30a6\u30e9\u30b8\u30df\u30fc\u30eb\u30fb\u30a6\u30a9\u30b8\u30e7\u30a6\u30c9\u30b9\u30ad\u30fc|2006\u5e74\uff1a\u30a2\u30f3\u30c9\u30ec\u30a4\u30fb\u30aa\u30ab\u30f3\u30af\u30fc\u3001\u30b0\u30ea\u30b4\u30ea\u30fb\u30da\u30ec\u30eb\u30de\u30f3\u3001\u30c6\u30ec\u30f3\u30b9\u30fb\u30d4\u30fc\u30d7\u30eb\u3001\u30a6\u30a7\u30f3\u30c7\u30ea\u30f3\u30fb\u30f4\u30a7\u30eb\u30ca\u30fc|2010\u5e74\uff1aElon Lindenstrauss\u3001Lynstrauss\u3001B\u1ea3oCh\u00e2u\u3001Stanislaw Smirnew\u3001C\u00e9dricVillani|2014\u5e74\uff1aArtur\u00e1vila\u3001Manjul Bhargava\u3001Martin Haiter\u3001Maryam Mirzakhani |2018\uff1aCaucher Birrkar\u3001Alessusio Figalli\u3001Peter Scholze\u3001Akshay Venkatesh |2022\u5e74\uff1a\u30d2\u30e5\u30fc\u30b4\u30fb\u30c9\u30a5\u30a4\u30cb\u30eb\u30fb\u30b3\u30d4\u30f3\u3001\u30b8\u30e5\u30fc\u30f3\u30fb\u30cf\u30c3\u3001\u30b8\u30a7\u30fc\u30e0\u30ba\u30fb\u30e1\u30a4\u30ca\u30fc\u30c9\u3001\u30e1\u30ea\u30fc\u30ca\u30fb\u30f4\u30a3\u30be\u30d5\u30b9\u30ab        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/19705#breadcrumbitem","name":"\u30de\u30a4\u30b1\u30eb\u30fb\u30d5\u30e9\u30f3\u30b7\u30b9\u30fb\u30a2\u30c6\u30a3\u30e4 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]