Existence and deformability of topological Morse functions
Geometric Topology
2026-03-11 v1
Abstract
In the 1950s Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appear to be Morse-theoretic in nature, there is a topological Morse function implicit in the argument. Topological Morse functions are known to inherit most of the familiar properties of the usual (smooth) Morse functions, with two crucial exceptions: existence and deformability. This paper gives a simple construction of continuous families of topological Morse functions.
Cite
@article{arxiv.2508.03260,
title = {Existence and deformability of topological Morse functions},
author = {Ingrid Irmer},
journal= {arXiv preprint arXiv:2508.03260},
year = {2026}
}