Actions of large finite groups on manifolds

2023/03/14 by Ignasi Mundet i Riera, Riera, Ignasi Mundet i · 2 citations
Mathematics · #54H15 #57S17 #Advanced Topology and Set Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2303.07784

openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group G on a manifold X, these results provide information on the restriction of the action to a subgroup of G of index bounded above by a number depending only on X. Some of these results refer to the algebraic structure of the group, such as being abelian, or nilpotent, or admitting a generating subset of controlled size; other results refer to the geometry of the action, e.g. to the existence of fixed points, to the collection of stabilizer subgroups, or to the action on cohomology.

Cited by

• Finite abelian group actions on weakly Lefschetz cohomologically symplectic manifolds
• Iterated finite group actions on closed connected aspherical manifolds

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