Witten deformation using Lie groupoids

Omar Mohsen

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arXiv · 1903.11583

Witten deformation using Lie groupoids

Omar Mohsen

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Abstract

We express Witten's deformation of Morse functions using deformation to the normal cone and $C^*$-modules. This allows us to obtain asymptotics of the `large eigenvalues'. Our methods extend to Morse functions along a foliation. We construct the Witten deformation using any generic function on an arbitrary foliation on a compact manifold and establish the compactness of its resolvent. When the foliation has a holonomy invariant transverse measure we show that our result implies Morse inequalities obtained by Connes and Fack in a slightly more general situation.

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BibTeX RIS

Omar Mohsen. 2019-03-27. Witten deformation using Lie groupoids. https://arxiv.org/abs/1903.11583

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