Morse theory without nondegeneracy

We describe an extension of Morse theory to smooth functions on compact Riemannian manifolds, without any nondegeneracy assumptions except that the critical locus must have only finitely many connected components.

Bibliographic Details
Main Authors: Kirwan, F, Penington, G
Format: Working paper
Language:English
Published: University of Oxford 2020
Description
Summary:We describe an extension of Morse theory to smooth functions on compact Riemannian manifolds, without any nondegeneracy assumptions except that the critical locus must have only finitely many connected components.