The Dowker theorem via discrete Morse theory
Combinatorics
2024-07-23 v1 Algebraic Topology
Abstract
The Dowker theorem is a classical result in the topology of finite spaces, claiming that any binary relation between two finite spaces defines two homotopy-equivalent complexes (the Dowker complexes). Recently, Barmak strengthened this to a simple-homotopy-equivalence. We reprove Barmak's result using a combinatorial argument that constructs an explicit acyclic matching in the sense of discrete Morse theory.
Cite
@article{arxiv.2407.15454,
title = {The Dowker theorem via discrete Morse theory},
author = {Morten Brun and Darij Grinberg},
journal= {arXiv preprint arXiv:2407.15454},
year = {2024}
}
Comments
20 pages. Comments are appreciated!