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arXiv · 2405.08653

The Connectedness Homomorphism between Discrete Morse Complexes

Chong Zheng
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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.

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Chong Zheng. 2024-07-12. The Connectedness Homomorphism between Discrete Morse Complexes. https://arxiv.org/abs/2405.08653

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