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arXiv · 2312.14032

The space of discrete Morse functions

Julian Brüggemann
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Abstract

In this work, we introduce a combinatorial-geometric model for the space of discrete Morse functions on any CW complex $X$. We relate this version of a space of discrete Morse functions to the space of cellular filtrations of $X$ and discuss its relationship to various concepts such as smooth Morse theory, Cerf theory, complexes of discrete Morse matchings, and induced merge trees and barcodes.

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Julian Brüggemann. 2023-12-21. The space of discrete Morse functions. https://arxiv.org/abs/2312.14032

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