Connecting Discrete Morse Functions via Birth-Death Transitions

Fuente: arXiv
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Autore principale: Zheng, Chong
Natura: Preprint
Pubblicazione: 2025
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_version_ 1866912585289302016
author Zheng, Chong
author_facet Zheng, Chong
contents We study transformations between discrete Morse functions on a finite simplicial complex via birth-death transitions--elementary chain maps between discrete Morse complexes that either create or cancel pairs of critical simplices. We prove that any two discrete Morse functions $f_1$, $f_2$ on a finite simplicial complex $K$ are linked by a finite sequence of such transitions.As applications, we present alternative proofs of several of Forman's fundamental results in discrete Morse theory and study the topology of the space of discrete Morse functions.
format Preprint
id arxiv_https___arxiv_org_abs_2508_15736
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Connecting Discrete Morse Functions via Birth-Death Transitions
Zheng, Chong
Combinatorics
Algebraic Topology
General Topology
We study transformations between discrete Morse functions on a finite simplicial complex via birth-death transitions--elementary chain maps between discrete Morse complexes that either create or cancel pairs of critical simplices. We prove that any two discrete Morse functions $f_1$, $f_2$ on a finite simplicial complex $K$ are linked by a finite sequence of such transitions.As applications, we present alternative proofs of several of Forman's fundamental results in discrete Morse theory and study the topology of the space of discrete Morse functions.
title Connecting Discrete Morse Functions via Birth-Death Transitions
topic Combinatorics
Algebraic Topology
General Topology
url https://arxiv.org/abs/2508.15736