Polyhedral Representation of Discrete Morse Functions on Regular CW Complexes and Posets
Combinatorics
2010-08-24 v1 Geometric Topology
Abstract
It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical points. The proof is stated in terms of discrete Morse functions on a class of posets that is slightly broader than the class of face posets of finite regular CW complexes.
Keywords
Cite
@article{arxiv.1008.3724,
title = {Polyhedral Representation of Discrete Morse Functions on Regular CW Complexes and Posets},
author = {Ethan D. Bloch},
journal= {arXiv preprint arXiv:1008.3724},
year = {2010}
}