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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Witten deformation for even dimensional conformally conic manifolds


Author: Ursula Ludwig
Journal: Trans. Amer. Math. Soc. 365 (2013), 885-909
MSC (2010): Primary 35A20; Secondary 57R70
Published electronically: July 2, 2012
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05651-0
PII: S 0002-9947(2012)05651-0
Keywords: Stratified Morse theory, conic singularities, Witten deformation
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.
Article copyright: © Copyright 2012 American Mathematical Society