Actions of large finite groups on aspherical manifolds

2024/07/18 by Jordi Daura Serrano, Serrano, Jordi Daura · 2 citations
Mathematics · #22E40 #54H15 #57S17 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2407.13602

openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study actions of finite groups on closed connected aspherical manifolds. Under some assumptions on the outer automorphism group of the fundamental group of a closed connected aspherical manifold M, we prove that the homeomorphism group of M is Jordan, we bound the discrete degree of symmetry of M and obtain a rigidity result, and we study the number of stabilizers of finite group actions on M. Thereafter, we show that closed connected aspherical locally homogeneous spaces H∖ G/Γ satisfy the necessary hypothesis on the outer automorphism group of the fundamental group.

Cited by

• Iterated finite group actions on closed connected aspherical manifolds
• Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds

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