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 $X$....

Descripción completa

Detalles Bibliográficos
Autor: Mundet i Riera, Ignasi
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2024
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/217220
Acceso en línea:https://hdl.handle.net/2445/217220
Access Level:acceso abierto
Palabra clave:Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
Descripción
Sumario: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.