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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}
}

Comments

20 pages

R2 v1 2026-06-28T16:27:02.848Z