Actions of large finite groups on manifolds

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 $X$....

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Bibliographic Details
Author: Mundet i Riera, Ignasi
Format: article
Status:Versión aceptada para publicación
Publication Date:2024
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/217220
Online Access:https://hdl.handle.net/2445/217220
Access Level:Open access
Keyword:Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
Description
Summary: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.