Discrete Morse Theory for Weighted Simplicial Complexes
Algebraic Topology
2020-02-05 v3
Abstract
In this paper, we study Forman's discrete Morse theory in the context of weighted homology. We develop weighted versions of classical theorems in discrete Morse theory. A key difference in the weighted case is that simplicial collapses do not necessarily preserve weighted homology. We work out some sufficient conditions for collapses to preserve weighted homology, as well as study the effect of elementary removals on weighted homology. An application to sequence analysis is included, where we study the weighted ordered complexes of sequences.
Keywords
Cite
@article{arxiv.1901.01716,
title = {Discrete Morse Theory for Weighted Simplicial Complexes},
author = {Chengyuan Wu and Shiquan Ren and Jie Wu and Kelin Xia},
journal= {arXiv preprint arXiv:1901.01716},
year = {2020}
}
Comments
19 pages, to appear in Topology and its Applications