The Witten deformation for even dimensional conformally conic manifolds
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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.References
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Additional Information
- Ursula Ludwig
- Affiliation: Mathematisches Institut, Universität Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany
- Email: ursula.ludwig@math.uni-freiburg.de
- Received by editor(s): July 29, 2010
- Received by editor(s) in revised form: May 25, 2011
- Published electronically: July 2, 2012
- Additional Notes: The author was supported in part by SFB 647.
- © Copyright 2012 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 365 (2013), 885-909
- MSC (2010): Primary 35A20; Secondary 57R70
- DOI: https://doi.org/10.1090/S0002-9947-2012-05651-0
- MathSciNet review: 2995377