Contractibility of the orbit space of a saturated fusion system after Steinberg

2023/12/31 by Omar Dennaoui, Dennaoui, Omar, Jonathon Villareal +1
Computer Science · Mathematics · #Advanced Operator Algebra Research #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2401.00531

openalex publication_date 2023/12/31 · openalex created_date 2024/01/03 · openalex updated_date 2026/07/28

Abstract

Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial p-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering more general versions of the theorem that were already known. In particular, following a strategy of Libman, we give a discrete Morse theoretic argument for the contractibility of the orbit space of a saturated fusion system.

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