English

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 XX. We relate this version of a space of discrete Morse functions to the space of cellular filtrations of XX 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