The Witten deformation for even dimensional spaces with cone-like singularities and admissible Morse functions
详细信息 查看全文
- 作者：Ursula Ludwig
- 刊名：Comptes Rendus Mathematique
- 出版年：2010
- 出版时间：August 2010
- 年：2010
- 卷：348
- 期：15-16
- 页码：915-918
- 全文大小：131 K
文摘
In this Note we generalise the Witten deformation to even dimensional Riemannian manifolds with cone-like singularities X and certain functions f, which we call admissible Morse functions. As a corollary we get Morse inequalities for the L2-Betti numbers of X. The contribution of a singular point p of X to the Morse inequalities can be expressed in terms of the intersection cohomology of the local Morse datum of f at p. The definition of the class of functions which we study here is inspired by stratified Morse theory as developed by Goresky and MacPherson. However the setting here is different since the spaces considered here are manifolds with cone-like singularities instead of Whitney stratified spaces.