The Witten deformation for even dimensional conformally conic manifolds

Ludwig, Ursula

doi:10.1090/S0002-9947-2012-05651-0

The Witten deformation for even dimensional conformally conic manifolds
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Trans. Amer. Math. Soc. 365 (2013), 885-909 Request permission

Abstract:

The goal of this article is to generalise the Witten deformation to even dimensional conformally conic manifolds $X$ and a class of functions $f: X \to \mathbb R$ called admissible Morse functions. We get Morse inequalities relating the $\mathrm {L}^2$-Betti numbers of $X$ with the number of critical points of the function $f$. Hereby 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 data of $f$ at $p$. The definition of an admissible Morse function is inspired by stratified Morse theory as developed by Goresky and MacPherson.

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