[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4353#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4353","headline":"\u4ea4\u53c9\u5f62\u5f0f (4\u6b21\u5143\u591a\u69d8\u4f53) – Wikipedia","name":"\u4ea4\u53c9\u5f62\u5f0f (4\u6b21\u5143\u591a\u69d8\u4f53) – Wikipedia","description":"\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\u5411\u304d\u4ed8\u3051\u3089\u308c\u305f\u30b3\u30f3\u30d1\u30af\u30c84\u6b21\u5143\u591a\u69d8\u4f53\u4e0a\u306e\u4ea4\u53c9\u5f62\u5f0f\uff08\u3053\u3046\u3055\u3051\u3044\u3057\u304d\u3001\u82f1: intersection form\uff09\u306f\u30014\u6b21\u5143\u591a\u69d8\u4f53\u306e\u7b2c2\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u4e0a\u306e\u7279\u5225\u306a\u5bfe\u79f0\u53cc\u7dda\u578b\u5f62\u5f0f\u3067\u3042\u308b\u3002\u3053\u306e\u5f62\u5f0f\u306f\u3001\u6ed1\u3089\u304b\u306a\u69cb\u9020\uff08\u82f1\u8a9e\u7248\uff09\u306e\u5b58\u5728\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u542b\u30804\u6b21\u5143\u591a\u69d8\u4f53\u306e\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u591a\u304f\u3092\u53cd\u6620\u3057\u3066\u3044\u308b\u3002 \u4ea4\u53c9\u5f62\u5f0f QM:H2(M;Z)\u00d7H2(M;Z)\u2192Z{displaystyle Q_{M}colon H^{2}(M;mathbb {Z} )times H^{2}(M;mathbb {Z} )to mathbb {Z} } \u306f\u3001 QM(a,b)=\u27e8a\u2323b,[M]\u27e9{displaystyle Q_{M}(a,b)=langle asmile","datePublished":"2020-04-04","dateModified":"2020-04-04","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki\/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\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/b\/b2\/Blue_question_mark.svg\/30px-Blue_question_mark.svg.png","height":"30","width":"30"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4353","about":["Wiki"],"wordCount":1351,"articleBody":"\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\u5411\u304d\u4ed8\u3051\u3089\u308c\u305f\u30b3\u30f3\u30d1\u30af\u30c84\u6b21\u5143\u591a\u69d8\u4f53\u4e0a\u306e\u4ea4\u53c9\u5f62\u5f0f\uff08\u3053\u3046\u3055\u3051\u3044\u3057\u304d\u3001\u82f1: intersection form\uff09\u306f\u30014\u6b21\u5143\u591a\u69d8\u4f53\u306e\u7b2c2\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u4e0a\u306e\u7279\u5225\u306a\u5bfe\u79f0\u53cc\u7dda\u578b\u5f62\u5f0f\u3067\u3042\u308b\u3002\u3053\u306e\u5f62\u5f0f\u306f\u3001\u6ed1\u3089\u304b\u306a\u69cb\u9020\uff08\u82f1\u8a9e\u7248\uff09\u306e\u5b58\u5728\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u542b\u30804\u6b21\u5143\u591a\u69d8\u4f53\u306e\u30c8\u30dd\u30ed\u30b8\u30fc\u306e\u591a\u304f\u3092\u53cd\u6620\u3057\u3066\u3044\u308b\u3002\u4ea4\u53c9\u5f62\u5f0fQM:H2(M;Z)\u00d7H2(M;Z)\u2192Z{displaystyle Q_{M}colon H^{2}(M;mathbb {Z} )times H^{2}(M;mathbb {Z} )to mathbb {Z} }\u306f\u3001QM(a,b)=\u27e8a\u2323b,[M]\u27e9{displaystyle Q_{M}(a,b)=langle asmile b,[M]rangle }\u306b\u3088\u308a\u4e0e\u3048\u3089\u308c\u308b\u30024\u6b21\u5143\u591a\u69d8\u4f53\u304c\u6ed1\u3089\u304b\u3067\u3082\u3042\u308b\u3068\u304d\u306f\u3001\u30c9\u30fb\u30e9\u30fc\u30e0\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u306b\u304a\u3044\u3066\u3001a \u3068 b \u304c 2-\u5f62\u5f0f \u03b1 \u3068 \u03b2 \u3068\u3057\u3066\u305d\u308c\u305e\u308c\u8868\u73fe\u3055\u308c\u3066\u3044\u308b\u3068\u304d\u3001\u4ea4\u53c9\u5f62\u5f0f\u306f\u3001\u7a4d\u5206Q(a,b)=\u222bM\u03b1\u2227\u03b2{displaystyle Q(a,b)=int _{M}alpha wedge beta }\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u306b \u2227{displaystyle wedge } \u306f\u30a6\u30a8\u30c3\u30b8\u7a4d\u3067\u3042\u308b\u3002\u5916\u7a4d\u4ee3\u6570\u3092\u53c2\u7167\u3002\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027[\u7de8\u96c6]\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027\u306b\u3088\u308a\u4ea4\u53c9\u5f62\u5f0f\u306e\u5e7e\u4f55\u5b66\u7684\u306a\u5b9a\u7fa9\u304c\u53ef\u80fd\u3067\u3042\u308b\u3002a \u3068 b \u306e\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u304c\u3001\u6a2a\u65ad\u7684\u306b\u4ea4\u53c9\u3059\u308b\u66f2\u9762\uff08\u3042\u308b\u3044\u306f 2-\u30b5\u30a4\u30af\u30eb\uff09A \u3068 B \u306b\u3088\u308a\u8868\u3055\u308c\u3066\u3044\u308b\u3068\u304d\u3001\u5404\u3005\u306e\u4ea4\u53c9\u70b9\u306f\u5411\u304d\u4ed8\u3051\u306b\u4f9d\u5b58\u3057\u3066\u91cd\u8907\u5ea6 +1 \u304b \u22121 \u3092\u6301\u3061\u3001QM(a,\u00a0b) \u306f\u3053\u308c\u3089\u306e\u91cd\u8907\u5ea6\u306e\u548c\u3068\u306a\u308b\u3002\u5f93\u3063\u3066\u3001\u4ea4\u53c9\u5f62\u5f0f\u3082\u7b2c2\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u4e0a\u306e\u30da\u30a2\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u6027\u306f\u3001\u4ea4\u53c9\u5f62\u5f0f\u304c\uff08\u6369\u308c\u306e\u9055\u3044\u3092\u9664\u3044\u3066\uff09\u30e6\u30cb\u30e2\u30b8\u30e5\u30e9\u30fc\uff08\u82f1\u8a9e\u7248\uff09\u3067\u3042\u308b\u3053\u3068\u3082\u610f\u5473\u3059\u308b\u3002\u6027\u8cea\u3068\u5fdc\u7528[\u7de8\u96c6]\u30a6\u30fc\u306e\u516c\u5f0f\uff08\u82f1\u8a9e\u7248\uff09\u306b\u3088\u308a\u3001\u30b9\u30d4\u30f3\u69cb\u9020\u3092\u6301\u30644\u6b21\u5143\u591a\u69d8\u4f53\u306f\u3001\u5076\u306e\u4ea4\u53c9\u5f62\u5f0f\u3001\u3064\u307e\u308a\u3001Q(x,x) \u306f\u3059\u3079\u3066\u306e x \u306b\u5bfe\u3057\u5076\u6570\u3068\u306a\u308b\u3002\u5358\u9023\u7d50\u306a 4\u6b21\u5143\u591a\u69d8\u4f53\uff08\u3042\u308b\u3044\u306f\u3088\u308a\u4e00\u822c\u7684\u306b\u7b2c\u4e00\u30db\u30e2\u30ed\u30b8\u30fc\u7fa4\u306b 2-torsion \u3092\u6301\u305f\u306a\u3044\u3088\u3046\u306a\u591a\u69d8\u4f53\uff09\u306b\u5bfe\u3057\u3066\u3001\u9006\u304c\u6210\u308a\u7acb\u3064\u3002\u4ea4\u53c9\u5f62\u5f0f\u306e\u7b26\u53f7\u306f\u91cd\u8981\u306a\u4e0d\u5909\u91cf\u3067\u3042\u308b\u30024\u6b21\u5143\u591a\u69d8\u4f53\u304c 5\u6b21\u5143\u591a\u69d8\u4f53\u306e\u5883\u754c\u3068\u306a\u308b\u3053\u3068\u3068\u3001\u4ea4\u53c9\u5f62\u5f0f\u306e\u7b26\u53f7\u304c 0 \u3067\u3042\u308b\u3053\u3068\u3068\u306f\u540c\u5024\u3067\u3042\u308b\u3002\u30d5\u30a1\u30f3\u30fb\u30c7\u30eb\u30fb\u30d6\u30ea\u30fc\u30b8\u306e\u88dc\u984c\uff08\u82f1\u8a9e\u7248\uff09(Van der Blij’s lemma)\u306f\u3001\u30b9\u30d4\u30f3 4\u6b21\u5143\u591a\u69d8\u4f53\u306f 8 \u500d\u6570\u306e\u7b26\u53f7\u3092\u6301\u3064\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3002\u5b9f\u969b\u3001\u30ed\u30db\u30ea\u30f3\u306e\u5b9a\u7406\u306f\u3001\u6ed1\u3089\u304b\u306a\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b9\u30d4\u30f3 4\u6b21\u5143\u591a\u69d8\u4f53\u306f 16 \u306e\u500d\u6570\u306e\u7b26\u53f7\u3092\u6301\u3064\u3068\u3044\u3046\u5b9a\u5024\u3067\u3042\u308b\u3002\u30de\u30a4\u30b1\u30eb\u30fb\u30d5\u30ea\u30fc\u30c9\u30de\u30f3(Michael Freedman)\u306f\u3001\u4ea4\u53c9\u5f62\u5f0f\u3092\u4f7f\u3044\u3001\u5358\u9023\u7d50\u306a\u4f4d\u76f8 4\u6b21\u5143\u591a\u69d8\u4f53\u3092\u5206\u985e\u3057\u305f\u3002\u6574\u6570\u4e0a\u306e\u4efb\u610f\u306e\u30e6\u30cb\u30e2\u30b8\u30e5\u30e9\u30fc\u5bfe\u79f0\u53cc\u7dda\u578b\u5f62\u5f0f Q \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u6574\u6570\u4fc2\u6570\u306e\u4ea4\u53c9\u5f62\u5f0f Q \u3092\u3082\u3064\u5358\u9023\u7d50\u306a 4\u6b21\u5143\u591a\u69d8\u4f53 M \u304c\u5b58\u5728\u3059\u308b\u3002Q \u304c\u5076\u3067\u3042\u308c\u3070\u3001\u4e00\u610f\u306b\u305d\u306e\u3088\u3046\u306a\u591a\u69d8\u4f53\u304c\u5b58\u5728\u3059\u308b\u3002Q \u304c\u5947\u3067\u3042\u308c\u3070\u30012\u3064\u306e\uff08\u5c11\u306a\u304f\u3068\u3082\u3072\u3068\u3064\u306e\u5bfe\uff09\u306f\u6ed1\u3089\u304b\u306a\u69cb\u9020\u3092\u6301\u305f\u306a\u3044\u591a\u69d8\u4f53\u304c\u5b58\u5728\u3059\u308b\u3002\u540c\u3058\u4ea4\u53c9\u5f62\u5f0f\u3092\u3082\u3064 2\u3064\u306e\u5358\u9023\u7d50\u306a\u9589\u3058\u305f 4\u6b21\u5143\u591a\u69d8\u4f53\u306f\u540c\u76f8\u3067\u3042\u308b\u3002\u5947\u306e\u5834\u5408\u306b\u306f\u30012\u3064\u306e\u591a\u69d8\u4f53\u306f\u3001\u30ab\u30fc\u30d3\u30fc\u30fb\u30b8\u30fc\u30d9\u30f3\u30de\u30f3\u4e0d\u5909\u91cf\u306b\u3088\u308a\u8b58\u5225\u3055\u308c\u308b\u3002\u30c9\u30ca\u30eb\u30c9\u30bd\u30f3\u306e\u5b9a\u7406\u306f\u3001\u6b63\u5b9a\u5024\u306a\u4ea4\u53c9\u5f62\u5f0f\u3092\u3082\u3064\u6ed1\u3089\u304b\u306a\u5358\u9023\u7d50\u3067\u3042\u308b 4\u6b21\u5143\u591a\u69d8\u4f53\u306f\u3001\u5bfe\u89d2\u5316\u53ef\u80fd\u306a\uff08\u30b9\u30ab\u30e9\u30fc 1\uff09\u306e\u4ea4\u53c9\u5f62\u5f0f\u3092\u6301\u3064\u3068\u3044\u3046\u5b9a\u7406\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u30d5\u30ea\u30fc\u30c9\u30de\u30f3\u306e\u5206\u985e\u306f\u3001\u6ed1\u3089\u304b\u3067\u306a\u3044 4\u6b21\u5143\u591a\u69d8\u4f53\uff08\u4f8b\u3048\u3070\u3001E8\u591a\u69d8\u4f53\uff08\u82f1\u8a9e\u7248\uff09(E8 manifold)\u304c\u591a\u6570\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u5411\u304d\u3064\u3051\u4e0d\u80fd\u591a\u69d8\u4f53[\u7de8\u96c6]Z\/2Z \u4fc2\u6570\u306b\u5bfe\u3059\u308b\u30dd\u30a2\u30f3\u30ab\u30ec\u53cc\u5bfe\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3068\u5168\u304f\u540c\u69d8\u306b\u3001Z \u3068\u3044\u3046\u3088\u308a\u3082 Z\/2Z \u4fc2\u6570\u306e\u4ea4\u53c9\u5f62\u5f0f\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3082\u5b58\u5728\u3059\u308b\u3002\u3053\u306e\u65b9\u6cd5\u306b\u3088\u308a\u3001\u5411\u304d\u3064\u3051\u4e0d\u80fd\u306a\u591a\u69d8\u4f53\u3082\u3001\u540c\u3058\u3088\u3046\u306b\u4ea4\u53c9\u5f62\u5f0f\u3092\u6301\u3064\u3002\u3082\u3061\u308d\u3093\u3001\u3053\u306e\u591a\u69d8\u4f53\u306e\u3069\u308c\u3082\u30c9\u30fb\u30e9\u30fc\u30e0\u30b3\u30db\u30e2\u30ed\u30b8\u30fc\u3067\u7406\u89e3\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Scorpan, A. (2005), The wild world of 4-manifolds, American Mathematical Society, ISBN\u00a00-8218-3749-4\u00a0"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki\/archives\/4353#breadcrumbitem","name":"\u4ea4\u53c9\u5f62\u5f0f (4\u6b21\u5143\u591a\u69d8\u4f53) – Wikipedia"}}]}]