配边

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在数学中，配边（英文：cobordism 来自法文的 bord）是紧流形的等价关系。它使用边界的拓扑概念。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：

$\partial W=M\sqcup N$ .

配边缩写为 $(W;M,N)$ 。M的配边类（cobordism class）是与M配边的所有流形的集合。 ^[1]

例子

最简单的例子是区间 I =[0,1]。这是 {0}和{1}这两个0-维流形的1-维配边。

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。

3维配边 $W=\mathbb {S} ^{1}\times \mathbb {D} ^{2}-\mathbb {D} ^{3}$ ； $M=\mathbb {S} ^{2}$ 是0-维流形； $N=\mathbb {S} ^{1}\times \mathbb {S} ^{1}$ 是2-环面（见割補理論）

参见

脚注

^ 若M和N是 $n$ 维的，则W是 $(n+1)$ 维的，而且这是 $(n+1)$ 维的配边。

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. 200–208 (1961).
Dieudonne, Jean Alexandre. A history of algebraic and differential topology.
Kosinski, Antoni A. Differential Manifolds. Dover Publications. October 19, 2007.
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. 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. 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）
Bordism on the Manifold Atlas.
B-Bordism Archive.is的存檔，存档日期2012-05-29 on the Manifold Atlas.

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