{"id":1177,"date":"2023-05-06T17:49:31","date_gmt":"2023-05-06T09:49:31","guid":{"rendered":"https:\/\/blog.vanabel.cn\/?p=1177"},"modified":"2023-05-06T20:15:59","modified_gmt":"2023-05-06T12:15:59","slug":"guanyuliantonghedeyixiejibenzhishi","status":"publish","type":"post","link":"https:\/\/blog.vanabel.cn\/?p=1177","title":{"rendered":"\u5173\u4e8e\u8fde\u901a\u548c\u7684\u4e00\u4e9b\u57fa\u672c\u77e5\u8bc6"},"content":{"rendered":"

1. \u8fde\u901a\u548c\u7684\u5b9a\u4e49<\/a><\/span>\n\n

\u5b9a\u4e49 1<\/span>.<\/span> \u5047\u8bbe$S_1,S_2$\u662f\u4e24\u4e2a\u66f2\u9762\uff0c$D_1\\subset S_1$, $D_2\\subset S_2$\u662f\u4e24\u4e2a\u5f00\u5706\u76d8\uff0c\u5373\u5b83\u4eec\u90fd\u540c\u80da\u4e8e\u6807\u51c6\u6b27\u6c0f\u5e73\u9762\u4e0a\u7684\u5355\u4f4d\u5706\u76d8\u3002\u5c06$D_i$\u5728$S_i$\u91cc\u7684\u8865\u96c6\u8bb0\u4f5c$S_i’$, \u5373$S_i’=S_i\\setminus D_i$, $i=1,2$. \u9009\u53d6\u540c\u80da\u6620\u5c04$h:\\partial D_1\\to \\partial D_2$, \u5219\u6211\u4eec\u53ef\u4ee5\u6784\u9020\u5982\u4e0b\u66f2\u9762$S_1\\#S_2$\uff1a\u5b83\u662f\u65e0\u4ea4\u5e76\u96c6$S_1\\sqcup S_2$\u5546\u6389\u7b49\u4ef7\u5173\u7cfb$\\sim$, $x\\sim y=h(x)$, \u5f97\u5230\u7684\u5546\u7a7a\u95f4\u3002\u5373$S_1\\#S_2=S_1\\sqcup S_2\/\\sim$.
\n<\/div>
\n\u53ef\u4ee5\u8bc1\u660e\u4e0a\u8ff0\u5b9a\u4e49\u662f\u826f\u597d\u7684\uff0c\u5373\u4e0d\u4f9d\u8d56\u4e8e\u5706\u76d8$D_1, D_2$\u4ee5\u53ca\u540c\u80da\u6620\u5c04$h$\u7684\u9009\u53d6\u3002
\n
\n2. \u4e00\u4e2a\u5178\u578b\u4f8b\u5b50<\/a><\/span>\n\n\u660e\u663e\u5730\uff0c\u6309\u7167\u5b9a\u4e49\u4efb\u4f55\u66f2\u9762\u548c\u7403\u9762\u7684\u8fde\u901a\u548c\u5c31\u662f\u5b83\u81ea\u5df1\u3002\u4e24\u4e2a\u73af\u9762\u7684\u8fde\u901a\u548c\u5c31\u662f\u4e8f\u683c\uff08\u6d1e\u7684\u4e2a\u6570\uff09\u4e3a2\u7684\u73af\u9762\u3001\u7ee7\u7eed\u548c\u4e00\u4e2a\u73af\u9762\u8fde\u901a\u548c\u5219\u5f97\u5230\u4e8f\u683c\u4e3a3\u7684\u73af\u9762\u3002\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/p>\n
\n
\"2-\u73af\u9762\"<\/a>
\u4e8f\u683c\u4e3a2\u7684\u73af\u9762<\/figcaption><\/figure>
\n
\"3-\u73af\u9762\"<\/a>
\u4e8f\u683c\u4e3a3\u7684\u73af\u9762<\/figcaption><\/figure>
\n
\"\u73af\u9762\u548c2\u73af\u9762\u7684\u8fde\u901a\u548c=3\u73af\u9762\"<\/a>
\u4e8f\u683c\u4e3a1\u7684\u73af\u9762\u548c\u4e8f\u683c\u4e3a2\u7684\u73af\u9762\u7684\u8fde\u901a\u548c<\/figcaption><\/figure><\/div>\n

3. \u4e00\u4e9b\u66f2\u9762\u7684\u8fde\u901a\u548c<\/a><\/span>\n\n\u56de\u5fc6Mobius\u5e26<\/a>\u662f\u5c06\u4e00\u4e2a\u957f\u65b9\u5f62\u7eb8\u6761\u7684\u4e00\u5bf9\u8fb9\u53cd\u5411\u7c98\u8d34\u800c\u5f97\u5230\u7684\uff08\u53e6\u4e00\u5bf9\u8fb9\u7528\u865a\u7ebf\u8868\u793a\uff09\u3002\u800c\u5c04\u5f71\u5e73\u9762\u662f\u5c06\u4e00\u4e2a\u6b63\u65b9\u5f62\u7eb8\u6761\u6216\u8005\u5355\u4f4d\u5706\u76d8\u7684\u8fb9\u754c\u4e0a\u5bf9\u5f84\u70b9\u7c98\u8d34\u800c\u5f97\u7684\u66f2\u9762\u3002
\n\u800cKlein\u74f6\u53ef\u4ee5\u89c6\u4e3a\u5c06\u4e00\u4e2a\u957f\u65b9\u5f62\u7eb8\u6761\u7684\u4e00\u5bf9\u5bf9\u8fb9\u540c\u5411\u7c98\u8d34\u3001\u53e6\u4e00\u5bf9\u5bf9\u8fb9\u53cd\u5411\u7c98\u8d34\u800c\u5f97\u5230\u7684\u3002\u7528\u56fe\u793a\u8868\u793a\u5982\u4e0b\uff1a
\n

\"Mobius\u5e26\"<\/a>
Mobius\u5e26
<\/figcaption><\/figure>
\n
\"construction-of-the-projective-plane.png\"<\/a>
\u5c04\u5f71\u5e73\u9762
<\/figcaption><\/figure>
\n
\"Glue-Klein-bottle.png\"<\/a>
Klein\u74f6
<\/figcaption><\/figure>
\n
\u4f8b\u5b50 1<\/span>.<\/span> \u4e24\u4e2a\u5c04\u5f71\u5e73\u9762\u7684\u8fde\u901a\u548c\u662fKlein\u74f6\u3002
\n<\/div>
\n
\u8bc1\u660e<\/span>.<\/span> \u8fd9\u4e2a\u8bc1\u660e\u4ee5\u53ca\u5176\u4e2d\u7528\u5230\u7684\u56fe\u7247\u90fd\u6765\u81eaConnected sum of projective plane \u2245 Klein bottle<\/a>. \u4e8b\u5b9e\u4e0a\uff0c\u4ece\u56fe\u6211\u4eec\u77e5\u9053\uff0cKlein\u74f6\u662f\u4e24\u4e2aMobius\u5e26\u7c98\u8d34\u800c\u5f97\u3002
\n
\"Connect-sum-of-two-projective-plane.png\"<\/a>
Klein\u74f6\u7684\u5206\u89e3
<\/figcaption><\/figure>
\n\u800c\u5c04\u5f71\u5e73\u9762\u6316\u6389\u5706\u76d8\u540c\u80da\u4e8eMobius\u5e26\u3002
\n
\"Projective-plane-minus-disc.png\"<\/a>
\u5c04\u5f71\u5e73\u9762\u6316\u6389\u5706\u76d8
<\/figcaption><\/figure>
\n<\/div>
\n
\u4f8b\u5b50 2<\/span>.<\/span> \u4e09\u4e2a\u5c04\u5f71\u5e73\u9762\u7684\u8fde\u901a\u548c\u662f\u4e00\u4e2a\u73af\u9762\u548c\u4e00\u4e2a\u5c04\u5f71\u5e73\u9762\u7684\u8fde\u901a\u548c\u3002
\n<\/div>
\n
\u8bc1\u660e<\/span>.<\/span> \u53c2\u8003Nigel Hitchin\u5173\u4e8eGeometry of Surfaces<\/a>\u7684\u8bb2\u4e49\uff0cProp.~2.1.
\n<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"

1. \u8fde\u901a\u548c\u7684\u5b9a\u4e49 \u5b9a\u4e49 1. \u5047\u8bbe$S_1,S_2$\u662f\u4e24\u4e2a\u66f2\u9762\uff0c$D_1\\subset S_1… \u7ee7\u7eed\u9605\u8bfb\u5173\u4e8e\u8fde\u901a\u548c\u7684\u4e00\u4e9b\u57fa\u672c\u77e5\u8bc6<\/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":[204],"class_list":["post-1177","post","type-post","status-publish","format-standard","hentry","category-math","tag-liantonghe-qumian-banqun-sheyingpingmian-mobiusdai-kleinping-huanmian-qiumian","entry"],"_links":{"self":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1177","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=1177"}],"version-history":[{"count":41,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1177\/revisions"}],"predecessor-version":[{"id":1240,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=\/wp\/v2\/posts\/1177\/revisions\/1240"}],"wp:attachment":[{"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.vanabel.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}