Existence and deformability of topological Morse functions

Ingrid Irmer

doi:10.1017/s0004972725100518

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arXiv · 2508.03260

Existence and deformability of topological Morse functions

Ingrid Irmer

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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.

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Ingrid Irmer. 2025-08-05. Existence and deformability of topological Morse functions. https://doi.org/10.1017/s0004972725100518

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