Morse inequalities for noncompact manifolds

Tsuyoshi Kato, Daisuke Kishimoto, Mitsunobu Tsutaya

Published 2024-11-07Version 1

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.