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配邊

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(W; M, N)的配邊

數學中,配邊英文cobordism 來自法文bord流形等價關係。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

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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。

Pair of pants的配邊

如果MN是兩個圓, 那麼MN 的不交並是pair of pants(W)的邊界。所以pair of pants是M和N的配邊。

3維配邊 是0-維流形; 是2-環面 (見割補理論

參見

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腳註

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  1. ^ 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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