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。
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。
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。
（见割補理論）]]
参见
- 陈类
- 莫尔斯理论
脚注
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.
*
- 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）
- [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] on the Manifold Atlas.
*
评论 (0)