[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/6400#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/6400","headline":"\u57fa\u672c\u985e – Wikipedia","name":"\u57fa\u672c\u985e – Wikipedia","description":"\u985e\u4f53\u8ad6\u306e\u57fa\u672c\u985e\u306b\u3064\u3044\u3066\u306f\u300c\u985e\u69cb\u6210\uff08\u82f1\u8a9e\u7248\uff09(class formation) \u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002 \u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u57fa\u672c\u985e”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082009\u5e7412\u6708\uff09 \u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002 \u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u57fa\u672c\u985e(fundamental class)\u306f\u3001\u5411\u304d\u3065\u3051\u3089\u308c\u305f\u591a\u69d8\u4f53 M \u306b\u4ed8\u968f\u3059\u308b\u30db\u30e2\u30ed\u30b8\u30fc\u985e [M] \u3067\u3042\u308a\u3001\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4 Hr(M;Z)\u2245Z{displaystyle","datePublished":"2018-07-31","dateModified":"2018-07-31","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/5f\/Disambig_gray.svg\/25px-Disambig_gray.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/5\/5f\/Disambig_gray.svg\/25px-Disambig_gray.svg.png","height":"19","width":"25"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/6400","about":["Wiki"],"wordCount":3378,"articleBody":"\u985e\u4f53\u8ad6\u306e\u57fa\u672c\u985e\u306b\u3064\u3044\u3066\u306f\u300c\u985e\u69cb\u6210\uff08\u82f1\u8a9e\u7248\uff09(class formation) \u300d\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u57fa\u672c\u985e”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082009\u5e7412\u6708\uff09\u539f\u6587\u3068\u6bd4\u3079\u305f\u7d50\u679c\u3001\u3053\u306e\u8a18\u4e8b\u306b\u306f\u591a\u6570\uff08\u5c11\u306a\u304f\u3068\u30825\u500b\u4ee5\u4e0a\uff09\u306e\u8aa4\u8a33\u304c\u3042\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u60c5\u5831\u306e\u5229\u7528\u306b\u306f\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u6b63\u78ba\u306a\u8868\u73fe\u306b\u6539\u8a33\u3067\u304d\u308b\u65b9\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002\u6570\u5b66\u306b\u304a\u3044\u3066\u3001\u57fa\u672c\u985e(fundamental class)\u306f\u3001\u5411\u304d\u3065\u3051\u3089\u308c\u305f\u591a\u69d8\u4f53 M \u306b\u4ed8\u968f\u3059\u308b\u30db\u30e2\u30ed\u30b8\u30fc\u985e [M] \u3067\u3042\u308a\u3001\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4 Hr(M;Z)\u2245Z{displaystyle H_{r}(M;mathbf {Z} )cong mathbf {Z} } \u306e\u751f\u6210\u5b50\u306b\u5bfe\u5fdc\u3059\u308b\u3002\u57fa\u672c\u985e\u306f\u3001\u591a\u69d8\u4f53\u306e\u9069\u5207\u306a\u4e09\u89d2\u5206\u5272\u306e\u6700\u9ad8\u6b21\u6570\u306e\u5358\u4f53\u306e\u5411\u304d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002Table of Contents\u9589\u591a\u69d8\u4f53\u3001\u5411\u304d\u4ed8\u3051\u53ef\u80fd\u591a\u69d8\u4f53[\u7de8\u96c6]\u30b9\u30c6\u30a3\u30fc\u30d5\u30a7\u30eb\u30fb\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u985e[\u7de8\u96c6]\u5883\u754c\u306e\u3042\u308b\u5834\u5408[\u7de8\u96c6]\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027[\u7de8\u96c6]\u53c2\u7167\u9805\u76ee[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]\u9589\u591a\u69d8\u4f53\u3001\u5411\u304d\u4ed8\u3051\u53ef\u80fd\u591a\u69d8\u4f53[\u7de8\u96c6]M \u304c\u6b21\u5143 n \u306e\u9023\u7d50\u306a\u5411\u304d\u4ed8\u3051\u53ef\u80fd\u306a\u9589\u591a\u69d8\u4f53\u3068\u3059\u308b\u3068\u3001\u6700\u9ad8\u6b21\u306e\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306f\u7121\u9650\u5de1\u56de\u7fa4 Hn(M,Z)\u2245Z{displaystyle H_{n}(M,mathbf {Z} )cong mathbf {Z} }   \u3067\u3042\u308a\u3001\u3053\u306e\u591a\u69d8\u4f53 M \u306e\u5411\u304d\u306f\u751f\u6210\u5b50\u3092\u9078\u3076\u3053\u3068\u3001\u3064\u307e\u308a\u3001\u540c\u578b Z\u2192Hn(M,Z){displaystyle mathbf {Z} to H_{n}(M,mathbf {Z} )} \u3092\u9078\u3076\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u751f\u6210\u5b50\u3092\u57fa\u672c\u985e(fundamental class)\u3068\u547c\u3076\u3002M \u304c\u5358\u9023\u7d50\u3067\u306a\u3051\u308c\u3070\u3001\u57fa\u672c\u985e\u306f\u3001\uff08\u5404\u3005\u306e\u6210\u5206\u306e\u5411\u304d\u4ed8\u3051\u306b\u5bfe\u5fdc\u3057\u305f\uff09\u5404\u3005\u306e\u9023\u7d50\u6210\u5206\u306e\u57fa\u672c\u985e\u306e\u76f4\u548c\u3067\u3042\u308b\u3002\u30c9\u30fb\u30e9\u30fc\u30e0\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u3068\u306e\u95a2\u4fc2\u3067\u306f\u3001\u57fa\u672c\u985e\u306f\u300cM \u4e0a\u306e\u7a4d\u5206\u300d\u3092\u8868\u73fe\u3059\u308b\u3002\u3059\u306a\u308f\u3061\u3001\u6ed1\u3089\u304b\u306a\u591a\u69d8\u4f53 M \u306b\u5bfe\u3057\u3066\u3001n-\u5f62\u5f0f \u03c9 \u306f\u3001\u57fa\u672c\u985e\u3068\u30da\u30a2  \u27e8\u03c9,[M]\u27e9=\u222bM\u03c9{displaystyle langle omega ,[M]rangle =int _{M}omega }\u3068\u3068\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u306f M \u4e0a\u306e \u03c9 \u306e\u7a4d\u5206\u3067\u3042\u308a\u3001\u03c9 \u306e\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u985e\u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u3002\u30b9\u30c6\u30a3\u30fc\u30d5\u30a7\u30eb\u30fb\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u985e[\u7de8\u96c6]M \u304c\u5411\u304d\u4ed8\u3051\u4e0d\u80fd\u3067\u3042\u308c\u3070\u3001\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306f\u7121\u9650\u5de1\u56de\u7fa4\u3067\u306f\u306a\u304f\uff1a  Hn(M,Z)\u2246Z{displaystyle H_{n}(M,mathbf {Z} )ncong mathbf {Z} } \u3001M \u306e\u5411\u304d\u4ed8\u3051\u3092\u5b9a\u7fa9\u3067\u304d\u306a\u3044\u3002\u5b9f\u969b\u3001\u5411\u304d\u4ed8\u3051\u4e0d\u80fd\u591a\u69d8\u4f53\u4e0a\u306e\u5fae\u5206 n-\u5f62\u5f0f\u3092\u7a4d\u5206\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002  \u3059\u3079\u3066\u306e\u9589\u591a\u69d8\u4f53\u306f Z2{displaystyle mathbf {Z} _{2}}-\u5411\u304d\u4ed8\u3051\u53ef\u80fd\u3067\u3042\u308a\u3001\uff08M \u304c\u9023\u7d50\u3067\u3042\u308c\u3070\u3001\uff09Hn(M;Z2)\u2245Z2{displaystyle H_{n}(M;mathbf {Z} _{2})cong mathbf {Z} _{2}} \u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306b\u3001\u3059\u3079\u3066\u306e\u9589\u591a\u69d8\u4f53\u306f\u3001Z2{displaystyle mathbf {Z} _{2}}-\u5411\u304d\u3064\u3051\u3089\u308c\u3001\uff08\u4e00\u610f\u306b\u5411\u304d\u4ed8\u3051\u304c\u6c7a\u5b9a\u3067\u304d\uff09Z2{displaystyle mathbf {Z} _{2}}-\u57fa\u672c\u985e\u3092\u6301\u3064\u3002\u3053\u306e Z2{displaystyle mathbf {Z} _{2}}-\u57fa\u672c\u985e\u306f\u3001\u30b9\u30c6\u30a3\u30fc\u30d5\u30a7\u30eb\u30fb\u30db\u30a4\u30c3\u30c8\u30cb\u30fc\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u306b\u4f7f\u308f\u308c\u308b\u3002\u5883\u754c\u306e\u3042\u308b\u5834\u5408[\u7de8\u96c6]M \u304c\u5883\u754c\u3092\u6301\u3064\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u5411\u304d\u3064\u3051\u53ef\u80fd\u591a\u69d8\u4f53\u3067\u3042\u308c\u3070\u3001\u6700\u9ad8\u6b21\u76f8\u5bfe\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306f\u3001\u518d\u3073\u3001\u7121\u9650\u5de1\u56de\u7fa4 Hn(M,\u2202M)\u2245Z{displaystyle H_{n}(M,partial M)cong mathbf {Z} } \u3068\u306a\u308a\u3001\u9589\u591a\u69d8\u4f53\u3067\u3042\u308c\u3070\u57fa\u672c\u985e\u306e\u8003\u3048\u65b9\u304c\u76f8\u5bfe\u7684\u306a\u5834\u5408\u3078\u3082\u62e1\u5f35\u3067\u304d\u308b\u3002\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027[\u7de8\u96c6]\u3053\u306e\u7bc0\u306e\u52a0\u7b46\u304c\u671b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 \uff082008\u5e7412\u6708\uff09\u4efb\u610f\u306e\u30a2\u30fc\u30d9\u30eb\u7fa4 G{displaystyle G} \u3068\u975e\u8ca0\u3067\u3042\u308b\u6574\u6570 q\u22650{displaystyle qgeq 0} \u306b\u5bfe\u3057\u3001\u57fa\u672c\u985e\u3068 q{displaystyle q} -\u6b21\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306e\u30ad\u30e3\u30c3\u30d7\u7a4d\u3092\u3068\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u540c\u578b[M]\u2229:Hq(M;G)\u2192Hn\u2212q(M;G){displaystyle [M]cap :H^{q}(M;G)rightarrow H_{n-q}(M;G)}\u3092\u5f97\u308b\u3002\u3053\u306e\u540c\u578b\u306f\u3001\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027H\u2217(M,R)\u2192Hn\u2212\u2217(M,R){displaystyle H^{*}(M,R)to H_{n-*}(M,R)}\u3092\u3082\u305f\u3089\u3059\u3002\u307e\u305f\u3001\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027\u306f\u76f8\u5bfe\u7684\u306a\u5834\u5408\u306b\u3082\u62e1\u5f35\u3055\u308c\u308b\u3002\u3053\u306e\u7bc0\u306e\u52a0\u7b46\u304c\u671b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 \uff082008\u5e7412\u6708\uff09\u30ea\u30fc\u7fa4\u306e\u65d7\u591a\u69d8\u4f53\uff08\u82f1\u8a9e\u7248\uff09(flag variety)\u306e\u30d6\u30ea\u30e5\u30a2\u5206\u89e3\u306b\u304a\u3044\u3066\u3001\u57fa\u672c\u985e\u306f\u6700\u9ad8\u6b21\u5143\u30b7\u30e5\u30fc\u30d9\u30eb\u30c8\u80de\u4f53\uff08\u82f1\u8a9e\u7248\uff09(Schubert cell)\u3001\u3042\u308b\u3044\u306f\u3001\u540c\u3058\u3053\u3068\u3067\u3042\u308b\u304c\u3001\u30b3\u30af\u30bb\u30bf\u30fc\u7fa4\u306e\u6700\u4f4e\u5143\uff08\u82f1\u8a9e\u7248\uff09(longest element of a Coxeter group)\u306b\u5bfe\u5fdc\u3059\u308b\u3002\u53c2\u7167\u9805\u76ee[\u7de8\u96c6]\u5916\u90e8\u30ea\u30f3\u30af[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki6\/archives\/6400#breadcrumbitem","name":"\u57fa\u672c\u985e – Wikipedia"}}]}]