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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Detalhes bibliográficos
Autor: Mundet i Riera, Ignasi
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2024
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/217220
Acesso em linha:https://hdl.handle.net/2445/217220
Access Level:acceso abierto
Palavra-chave:Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
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spelling Actions of large finite groups on manifoldsMundet i Riera, IgnasiVarietats (Matemàtica)Grups de transformacionsManifolds (Mathematics)Transformation groupsIn 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.2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/217220Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1142/S0129167X2441012XInternational Journal of Mathematics, 2024, vol. 35, num.9https://doi.org/10.1142/S0129167X2441012X(c) World Scientific Publishing, 2024info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2172202026-05-27T06:46:51Z
dc.title.none.fl_str_mv Actions of large finite groups on manifolds
title Actions of large finite groups on manifolds
spellingShingle Actions of large finite groups on manifolds
Mundet i Riera, Ignasi
Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
title_short Actions of large finite groups on manifolds
title_full Actions of large finite groups on manifolds
title_fullStr Actions of large finite groups on manifolds
title_full_unstemmed Actions of large finite groups on manifolds
title_sort Actions of large finite groups on manifolds
dc.creator.none.fl_str_mv Mundet i Riera, Ignasi
author Mundet i Riera, Ignasi
author_facet Mundet i Riera, Ignasi
author_role author
dc.subject.none.fl_str_mv Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
topic Varietats (Matemàtica)
Grups de transformacions
Manifolds (Mathematics)
Transformation groups
description 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.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/217220
url https://hdl.handle.net/2445/217220
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1142/S0129167X2441012X
International Journal of Mathematics, 2024, vol. 35, num.9
https://doi.org/10.1142/S0129167X2441012X
dc.rights.none.fl_str_mv (c) World Scientific Publishing, 2024
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) World Scientific Publishing, 2024
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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