Discrete Morse Theory on Digraphs
Combinatorics
2021-11-16 v2 Algebraic Topology
Abstract
In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using quasi-isomorphism between path complex and discrete Morse complex, we also prove a general sufficient condition for digraphs that the Morse functions satisfying this necessary and sufficient condition.
Cite
@article{arxiv.2102.10518,
title = {Discrete Morse Theory on Digraphs},
author = {Yong Lin and Chong Wang and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2102.10518},
year = {2021}
}