Morse inequalities for noncompact manifolds

Tsuyoshi Kato; Daisuke Kishimoto; Mitsunobu Tsutaya

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arXiv · 2411.04463

Morse inequalities for noncompact manifolds

Tsuyoshi Kato·Daisuke Kishimoto·Mitsunobu Tsutaya

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Abstract

We establish Morse inequalities for a noncompact manifold with a cocompact and properly discontinuous action of a discrete group, where Morse functions are not necessarily invariant under the group action. The inequalities are given in terms of the $L^2$-Betti numbers and functions on the acting group which describe rough configurations of critical points of a Morse function.

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Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya. 2024-11-07. Morse inequalities for noncompact manifolds. https://arxiv.org/abs/2411.04463

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