Some remarks on Morse theory for posets, homological Morse theory and\n finite manifolds

2010/07/12 by Elías Gabriel Minian, Minian, Elias Gabriel
Computer Science · Mathematics · #06A06 #52B70 #55P15 #55U05 #57Q05 #57Q10 #57Q15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1007.1930

openalex publication_date 2010/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a version of discrete Morse theory for posets. This theory\nstudies the topology of the order complexes K(X) of h-regular posets X from the\ncritical points of admissible matchings on X. Our approach is related to R.\nForman's discrete Morse theory for CW-complexes and generalizes Forman and\nChari's results on the face posets of regular CW-complexes. We also introduce a\nhomological variant of the theory that can be used to study the topology of\ntriangulable homology manifolds by means of their order triangulations.\n

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