配边
此条目需要精通或熟悉相关主题的编者参与及协助编辑。 (2020年2月2日) |
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:
.
配边缩写为 。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。
参见
脚注
- ^ 若M和N是 维的,则W是 维的,而且这是 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.
- 谢尔盖·彼得罗维奇·诺维科夫, 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的存档,存档日期2012-05-29 on the Manifold Atlas.