数学中,配边英文cobordism 来自法文bord流形等价关系。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:

(W; M, N)的配边

.

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]

例子编辑

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。

 
Pair of pants的配边

如果MN是两个圆, 那么MN 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    是0-维流形;  是2-环面 (见割補理論

参见编辑

脚注编辑

  1. ^ 若M和N是 维的,则W是 维的,而且这是 维的配边。

参考文献编辑

  • 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存檔,存档日期2012-05-29 on the Manifold Atlas.