The space of discrete Morse functions
Algebraic Topology
2026-02-13 v2
Abstract
In this work, we introduce a combinatorial-geometric model for the space of discrete Morse functions on any CW complex . We relate this version of a space of discrete Morse functions to the space of cellular filtrations of 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.
Keywords
Cite
@article{arxiv.2312.14032,
title = {The space of discrete Morse functions},
author = {Julian Brüggemann},
journal= {arXiv preprint arXiv:2312.14032},
year = {2026}
}
Comments
38 pages, comments welcome