查看“︁配边”︁的源代码

{{expert|time=2020-02-02T03:18:25+00:00}}
[[File:Cobordism.svg|缩略图|(''W''; ''M'', ''N'')的配边]]
在[[数学]]中，'''配边'''（[[英文]]：'''cobordism''' 来自[[法文]]的 '''''[[wikt:bord|bord]]''）'''是[[紧空间|紧]][[流形]]的[[等价关系]]。它使用[[边界 (拓扑学)|边界]]的拓扑概念。若两个流形M和N的[[不交并]]是另一个流形W的边界，那么M和N这两个流形是配边的。此外M和N的配边是W：

<math>\partial W=M \sqcup N</math>.

配边缩写为 <math>(W; M, N)</math>。M的'''配边类（cobordism class）'''是与M配边的所有流形的[[集合 (数学)|集合]]。 <ref>若M和N是<math>n</math>维的，则W是<math>(n+1)</math>维的，而且这是<math>(n+1)</math>维的配边。</ref> 

== 例子 ==
最简单的例子是[[单位区间|区间]] ''I'' =[0,1]。这是 {0}和{1}这两个0-维流形的1-维配边。
[[File:Pair_of_pants_cobordism_(pantslike).svg|右|缩略图|[[Pair of pants]]的配边]]
如果''M'' 是[[圆]]，''N''是两个圆, 那么''M'' 和 ''N'' 的不交并是[[pair of pants]]（W）的边界。所以pair of pants是M和N的配边。
[[File:Cobordism.svg|缩略图|3维配边 <math>W = \mathbb{S}^1 \times \mathbb{D}^2 - \mathbb{D}^3</math>；<math>M = \mathbb{S}^2</math> 是0-维流形；<math>N = \mathbb{S}^1 \times \mathbb{S}^1</math> 是2-[[环面]] （见[[割補理論]]）]]

== 参见 ==

* [[陈类]]
* [[莫尔斯理论]]

== 脚注 ==
{{Reflist}}

== 参考文献 ==

* John Frank Adams, ''Stable homotopy and generalised homology'', Univ. Chicago Press (1974).
* Anosov, Dmitri; bordism
* [[迈克尔·阿蒂亚]], ''Bordism and cobordism'' Proc. Camb. Phil. Soc. 57, pp.&nbsp;200–208 (1961).
* Dieudonne, Jean Alexandre. A history of algebraic and differential topology.
* {{Cite document|title=Differential Manifolds|last=Kosinski|first=Antoni A.|date=October 19, 2007|publisher=Dover Publications|ref=harv|postscript=<!--None-->}}
* Madsen, Ib. The classifying spaces for surgery and cobordism of manifolds. [[普林斯顿]]
* [[约翰·米尔诺]]，A survey of cobordism theory.
* [[謝爾蓋·彼得羅維奇·諾維科夫]], ''Methods of algebraic topology from the point of view of cobordism theory'', Izv. Akad. Nauk SSSR Ser. Mat. '''31''' (1967), 855–951.
* [[列夫·庞特里亚金]], ''Smooth manifolds and their applications in homotopy theory'' American Mathematical Society Translations, Ser. 2, Vol. 11, pp.&nbsp;1–114 (1959).
* [[丹尼尔·奎伦]], ''On the formal group laws of unoriented and complex cobordism theory'' Bull. Amer. Math. Soc., 75 (1969) pp.&nbsp;1293–1298.
* Douglas Ravenel, ''Complex cobordism and stable homotopy groups of spheres'', Acad. Press (1986).
* Yuli Rudyak Cobordism.
* Yuli B. Rudyak, ''On Thom spectra, orientability, and (co)bordism'', Springer (2008).
* Robert E. Stong, ''Notes on cobordism theory'', Princeton Univ. Press (1968).
* Taimanov, Iskander. Topological library. Part 1: cobordisms
* [[勒内·托姆]], ''Quelques propriétés globales des variétés différentiables'', Commentarii Mathematici Helvetici 28, 17-86 (1954).
* Wall, C. T. C. Determination of cobordism ring. Annals of Mathematics（[[数学年刊]]）
* [https://web.archive.org/web/20110719102848/http://www.map.him.uni-bonn.de/Bordism Bordism] on the Manifold Atlas.
* [http://www.map.him.uni-bonn.de/B-Bordism B-Bordism] {{Webarchive|url=https://archive.today/20120529222452/http://www.map.him.uni-bonn.de/B-Bordism |date=2012-05-29 }} on the Manifold Atlas.

* 

[[Category:代数拓扑]]
[[Category:微分拓扑学]]