Morse theory of Bestvina-Brady type for posets and matchings

2022/05/23 by Minian, Elias Gabriel
#06A06 #55N31 #55P15 #55U05 #57Q05 #57Q70 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.11062

Abstract

We introduce a Morse theory for posets of Bestvina-Brady type combining matchings and height functions. This theory generalizes Forman's discrete Morse theory for regular CW-complexes and extends previous results on Morse theory for h-regular posets to all finite posets. We also develop a relative version of Morse theory which allows us to compare the topology of a poset with that of a given subposet.

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