The Connectedness Homomorphism between Discrete Morse Complexes
Combinatorics
2024-07-15 v2 Algebraic Topology
Abstract
Given two discrete Morse functions on a simplicial complex, we introduce the {\em connectedness homomorphism} between the corresponding discrete Morse complexes. This concept leads to a novel framework for studying the connectedness in discrete Morse theory at the chain complex level. In particular, we apply it to describe a discrete analogy to `cusp-degeneration' of Morse complexes. A precise comparison between smooth case and our discrete cases is also given.
Keywords
Cite
@article{arxiv.2405.08653,
title = {The Connectedness Homomorphism between Discrete Morse Complexes},
author = {Chong Zheng},
journal= {arXiv preprint arXiv:2405.08653},
year = {2024}
}
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20 pages