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math.AT2022
Star clusters in the Matching, Morse, and Generalized Morse complex
Connor Donovan, Nicholas A. Scoville
In this paper, we determine the homotopy type of the Morse complex and matching complex of multiple families of complexes by utilizing star cluster collapses and the Cluster Lemma.…
math.AT2019
On the homotopy and strong homotopy type of complexes of discrete Morse functions
Connor Donovan, Maxwell Lin, Nicholas A. Scoville
In this paper, we determine the homotopy type of the Morse complex of certain collections of simplicial complexes by studying dominating vertices or strong collapses. We show that…