配邊
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![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Cobordism.svg/220px-Cobordism.svg.png)
在數學中,配邊(英文:cobordism 來自法文的 bord)是緊流形的等價關係。它使用邊界的拓撲概念。若兩個流形M和N的不交並是另一個流形W的邊界,那麼M和N這兩個流形是配邊的。此外M和N的配邊是W:
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配邊縮寫為 。M的配邊類(cobordism class)是與M配邊的所有流形的集合。 [1]
例子
最簡單的例子是區間 I =[0,1]。這是 {0}和{1}這兩個0-維流形的1-維配邊。
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Pair_of_pants_cobordism_%28pantslike%29.svg/220px-Pair_of_pants_cobordism_%28pantslike%29.svg.png)
如果M 是圓,N是兩個圓, 那麼M 和 N 的不交並是pair of pants(W)的邊界。所以pair of pants是M和N的配邊。
![](http://images.weserv.nl/?url=//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Cobordism.svg/220px-Cobordism.svg.png)
參見
腳註
- ^ 若M和N是維的,則W是維的,而且這是維的配邊。
參考文獻
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- Bordism on the Manifold Atlas.
- B-Bordism Archive.is的存檔,存檔日期2012-05-29 on the Manifold Atlas.