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The Connectedness Homomorphism between Discrete Morse Complexes (2405.08653v2)
Published 14 May 2024 in math.CO and math.AT
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.