{"id":1537,"date":"2023-06-01T23:53:45","date_gmt":"2023-06-01T15:53:45","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=1537"},"modified":"2023-06-03T02:56:49","modified_gmt":"2023-06-02T18:56:49","slug":"guanyudaishutapuqumianfenleidinglizhongsanjiaopoufenzhuanhuanweijianhuaduobianxingdeyigelizi","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1537","title":{"rendered":"\u5173\u4e8e\u4ee3\u6570\u62d3\u6251\u66f2\u9762\u5206\u7c7b\u5b9a\u7406:I"},"content":{"rendered":"<p>\u66f2\u9762\u5206\u7c7b\u5b9a\u7406\u7684\u7b2c\u4e00\u6b65\u662f\u4f7f\u7528\u4e09\u89d2\u5256\u5206\uff0c\u5c06\u66f2\u9762\u8f6c\u5316\u4e3a\u7b80\u5355\u591a\u8fb9\u5f62\u3002Massey\u7684\u4e66\u4e0a\u5217\u4e3e\u4e86\u6b63\u65b9\u4f53\u7684\u4e09\u89d2\u5256\u5206\u8f6c\u6362\u4e3a\u591a\u8fb9\u5f62\u7684\u4f8b\u5b50\u3002\u8fd9\u91cc\uff0c\u6211\u4eec\u6765\u770b\u53e6\u4e00\u4e9b\u4f8b\u5b50\u3002\u5176\u57fa\u672c\u60f3\u6cd5\u662f\uff0c\u901a\u8fc7\u5bf9\u7ed9\u5b9a\u7684\u5256\u5206\u4e09\u89d2\u5f62\u91cd\u65b0\u7f16\u53f7$T_1,T_2,\\ldots, T_n$, \u4f7f\u5f97$T_i$\u4e0e$T_1,\\ldots, T_{i-1}$\u81f3\u5c11\u6709\u4e00\u6761\u516c\u5171\u8fb9, $i=2,3,\\ldots, n$.<br \/>\n<div class='latex_examp'><span class='latex_examp_h'>\u4f8b\u5b50 1<\/span> (<span class='latex_examp_name'>[<a href='#Massey1977Algebraic'>1<\/a>,Ex.~7.1, P.~21]<\/span>)<span class='latex_examp_h'>.<\/span> \u4e09\u89d2\u5256\u5206\u4e3a<\/p>\n<pre lang=\"text\">124 236 134 246\n367 347 469 459\n698 678 457 259\n289 578 358 125\n238 135\n<\/pre>\n<p><\/div><br \/>\n<!--more--><\/p>\n<p>\u901a\u8fc7\u4f5c\u56fe\uff0c\u5f97\u5230\u5256\u5206\u7684\u66f2\u9762\u5982\u56fe\u6240\u793a<\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-triangulation-1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1540\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-triangulation-1.png\" alt=\"\" width=\"564\" height=\"462\" srcset=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-triangulation-1.png 564w, https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-triangulation-1-300x246.png 300w\" sizes=\"auto, (max-width: 564px) 100vw, 564px\" \/><\/a><br \/>\n<!--\n<iframe loading=\"lazy\" src=\"https:\/\/www.geogebra.org\/classic\/du95tgrm?embed\" width=\"800\" height=\"600\" allowfullscreen style=\"border: 1px solid #e4e4e4;border-radius: 4px;\" frameborder=\"0\"><\/iframe>\n--><br \/>\n\u6700\u7ec8\u5f97\u5230\u7684\u7b80\u5316\u591a\u8fb9\u5f62\u4e3a<\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-simplified-polygon.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-1538\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-simplified-polygon.png\" alt=\"\" width=\"741\" height=\"758\" srcset=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-simplified-polygon.png 741w, https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey1977AlgebraicP21Ex7.1-simplified-polygon-293x300.png 293w\" sizes=\"auto, (max-width: 741px) 100vw, 741px\" \/><\/a><br \/>\n\u5373\u53ef\u7b49\u4ef7\u63cf\u8ff0\u4e3a<br \/>\n$$<br \/>\nab^{-1}cdebfgc^{-1}e^{-1}d^{-1}g^{-1}f^{-1}a^{-1}.<br \/>\n$$<br \/>\n<div class='latex_examp'><span class='latex_examp_h'>\u4f8b\u5b50 2<\/span> (<span class='latex_examp_name'>[<a href='#Massey1977Algebraic'>1<\/a>,Ex.~7.2, P.~21]<\/span>)<span class='latex_examp_h'>.<\/span> \u56db\u9762\u4f53\u7684\u8868\u9762\uff0c\u5176\u4e09\u89d2\u5256\u5206\u4e3a\uff1a<\/p>\n<pre lang=\"text\">\n123 234 341 412\n<\/pre>\n<p><\/div><br \/>\n\u901a\u8fc7\u4f5c\u56fe\uff0c\u6700\u7ec8\u5f97\u5230\u7684\u7b80\u5316\u591a\u8fb9\u5f62\u5982\u56fe\u6240\u793a\uff1a<\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.2.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.2.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.2.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.2.png\" class=\"aligncenter\" width=\"500\"\/><\/a><br \/>\n\u53ef\u7b49\u4ef7\u63cf\u8ff0\u4e3a<br \/>\n$$<br \/>\na^{-1}ab^{-1}bc^{-1}c.<br \/>\n$$<br \/>\n<div class='latex_examp'><span class='latex_examp_h'>\u4f8b\u5b50 3<\/span> (<span class='latex_examp_name'>[<a href='#Massey1977Algebraic'>1<\/a>,Ex.~7.3, P.~21]<\/span>)<span class='latex_examp_h'>.<\/span> \u5c04\u5f71\u5e73\u9762, \u5176\u4e09\u89d2\u5256\u5206\u4e3a\uff1a<\/p>\n<pre lang=\"text\">\n123 234 345 451 512\n136 246 356 416 526\n<\/pre>\n<p><\/div><br \/>\n\u901a\u8fc7\u4f5c\u56fe\uff0c<br \/>\n<a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.3-triangulation.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.3-triangulation.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.3-triangulation.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.3-triangulation.png\" class=\"aligncenter\" \/><\/a><\/p>\n<p><!--<iframe loading=\"lazy\" src=\"https:\/\/www.geogebra.org\/classic\/yse6m2jq?embed\" width=\"800\" height=\"600\" allowfullscreen style=\"border: 1px solid #e4e4e4;border-radius: 4px;\" frameborder=\"0\"><\/iframe>--><br \/>\n\u6211\u4eec\u77e5\u9053\u5176\u7b80\u5316\u591a\u8fb9\u5f62\u4e3a<br \/>\n<a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.3.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.3.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.3.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.3.png\" class=\"aligncenter\" \/><\/a><br \/>\n\u53ef\u7b49\u4ef7\u63cf\u8ff0\u4e3a<br \/>\n$$<br \/>\nabcabc<br \/>\n$$<br \/>\n<div class='latex_examp'><span class='latex_examp_h'>\u4f8b\u5b50 4<\/span> (<span class='latex_examp_name'>[<a href='#Massey1977Algebraic'>1<\/a>,Ex.~7.4, P.~21]<\/span>)<span class='latex_examp_h'>.<\/span> \u4e09\u89d2\u5256\u5206\u4e3a\uff1a<\/p>\n<pre lang=\"text\">\n124 235 346 457 561 672\n713 134 245 356 467 571\n126 237\n<\/pre>\n<p><\/div><br \/>\n\u4f5c\u56fe\u5f97\u5230<br \/>\n<!--\n  <iframe loading=\"lazy\" src=\"https:\/\/www.geogebra.org\/classic\/fnpqvqq5?embed\" width=\"800\" height=\"600\" allowfullscreen style=\"border: 1px solid #e4e4e4;border-radius: 4px;\" frameborder=\"0\"><\/iframe>\n--><\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.4-triangulation.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.4-triangulation.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.4-triangulation.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.4-triangulation.png\" class=\"aligncenter\" \/><\/a><br \/>\n\u5b83\u7684\u7b80\u5316\u591a\u8fb9\u5f62\u4e3a<br \/>\n$$abcdea^{-1}c^{-1}b^{-1}e^{-1}d^{-1}$$<br \/>\n\u5982\u56fe\u6240\u793a<\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.4-simplified-polygon.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.4-simplified-polygon.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.4-simplified-polygon.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.4-simplified-polygon.png\" class=\"aligncenter\" \/><\/a><\/p>\n<p><div class='latex_examp'><span class='latex_examp_h'>\u4f8b\u5b50 5<\/span> (<span class='latex_examp_name'>[<a href='#Massey1977Algebraic'>1<\/a>,Ex.~7.5, P.~21]<\/span>)<span class='latex_examp_h'>.<\/span> \u4e09\u89d2\u5256\u5206\u4e3a\uff1a<\/p>\n<pre lang=\"text\">\n123 256 341 451\n156 268 357 468\n167 275 374 476\n172 283 385 485\n<\/pre>\n<p><\/div><br \/>\n<!--\n<iframe loading=\"lazy\" src=\"https:\/\/www.geogebra.org\/classic\/r5mhr6d4?embed\" width=\"800\" height=\"600\" allowfullscreen style=\"border: 1px solid #e4e4e4;border-radius: 4px;\" frameborder=\"0\"><\/iframe>--><\/p>\n<p><a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.5-triangulation.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.5-triangulation.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.5-triangulation.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.5-triangulation.png\" class=\"aligncenter\" \/><\/a><\/p>\n<p>\u5f97\u5230\u7684\u7b80\u5316\u591a\u8fb9\u5f62\u4e3a<br \/>\n<!--\n  <iframe loading=\"lazy\" src=\"https:\/\/www.geogebra.org\/classic\/asjeffde?embed\" width=\"800\" height=\"600\" allowfullscreen style=\"border: 1px solid #e4e4e4;border-radius: 4px;\" frameborder=\"0\"><\/iframe>\n--><br \/>\n<a href=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.5-simplified-polygon.png\"><img decoding=\"async\" title=\"Massey_AlgebraicTopology_P21Ex7.5-simplified-polygon.png\" alt=\"Massey_AlgebraicTopology_P21Ex7.5-simplified-polygon.png\" src=\"https:\/\/blog.vanabel.cn\/wp-content\/uploads\/2023\/06\/Massey_AlgebraicTopology_P21Ex7.5-simplified-polygon.png\" class=\"aligncenter\" \/><\/a><\/p>\n<p>\u53ef\u7b49\u4ef7\u8868\u793a\u4e3a<br \/>\n$$<br \/>\nabcdeabcfe^{-1}d^{-1}f.<br \/>\n$$<\/p>\n<div class='bibtex'>\n\t<div class='bibtex_h'>\u53c2\u8003\u6587\u732e<\/div>\n\t<ol><li id='Massey1977Algebraic'><span class='bibtex_author'>W. Massey<\/span>, <a class='bibtex_title' target='_blank' href='http:\/\/www.google.com\/search?q=Algebraic topology: an introduction'>Algebraic topology: an introduction<\/a>, <span class='bibtex_series'>Graduate Texts in Mathematics, Vol. 56<\/span>, <span class='bibtex_publisher'>Springer-Verlag, New York-Heidelberg<\/span>, <span class='bibtex_year'>1977<\/span>. <span class='bibtex_page'>0---387<\/span>. <span class='bibtex_note'>Reprint of the 1967 edition<\/span>. MR<a class='bibtex_mrnumber' target='_blank' href='http:\/\/www.ams.org\/mathscinet-getitem?mr=0448331'>0448331<\/a><\/li><\/ol><\/div>","protected":false},"excerpt":{"rendered":"<p>\u66f2\u9762\u5206\u7c7b\u5b9a\u7406\u7684\u7b2c\u4e00\u6b65\u662f\u4f7f\u7528\u4e09\u89d2\u5256\u5206\uff0c\u5c06\u66f2\u9762\u8f6c\u5316\u4e3a\u7b80\u5355\u591a\u8fb9\u5f62\u3002Massey\u7684\u4e66\u4e0a\u5217\u4e3e\u4e86\u6b63\u65b9\u4f53\u7684\u4e09\u89d2\u5256\u5206\u8f6c\u6362\u4e3a\u591a\u8fb9&hellip; <a class=\"more-link\" href=\"https:\/\/blog.vanabel.cn\/?p=1537\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u5173\u4e8e\u4ee3\u6570\u62d3\u6251\u66f2\u9762\u5206\u7c7b\u5b9a\u7406:I<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[295,293],"class_list":["post-1537","post","type-post","status-publish","format-standard","hentry","category-math","tag-sanjiaopoufen","tag-daishutapu","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1537","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1537"}],"version-history":[{"count":28,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1537\/revisions"}],"predecessor-version":[{"id":1580,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1537\/revisions\/1580"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}