Discrete degree of symmetry of manifolds

We define the discrete degree of symmetry disc-sym $(X)$ of a closed $n$-manifold $X$ as the biggest $m \geq 0$ such that $X$ supports an effective action of $(\mathbb{Z} / r)^m$ for arbitrarily big values of $r$. We prove that if $X$ is connected then disc-sym $(X) \leq$ $3 n / 2$. We propose the q...

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Autor: Mundet i Riera, Ignasi
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/216593
Acceso en línea:https://hdl.handle.net/2445/216593
Access Level:acceso abierto
Palabra clave:Grups de transformacions
Topologia
Transformation groups
Topology
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spelling Discrete degree of symmetry of manifoldsMundet i Riera, IgnasiGrups de transformacionsTopologiaTransformation groupsTopologyWe define the discrete degree of symmetry disc-sym $(X)$ of a closed $n$-manifold $X$ as the biggest $m \geq 0$ such that $X$ supports an effective action of $(\mathbb{Z} / r)^m$ for arbitrarily big values of $r$. We prove that if $X$ is connected then disc-sym $(X) \leq$ $3 n / 2$. We propose the question of whether for every closed connected $n$-manifold $X$ the inequality disc-sym $(X) \leq n$ holds true, and whether the only closed connected $n$-manifold $X$ for which disc-sym $(X)=n$ is the torus $T^n$. We prove partial results providing evidence for an affirmative answer to this question.Springer Verlag2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/216593Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/https://doi.org/10.1007/s00031-024-09858-zTransformation Groups, 2024https://doi.org/https://doi.org/10.1007/s00031-024-09858-zcc by (c) Ignasi Mundet i Riera, 2024http://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2165932026-05-27T06:46:51Z
dc.title.none.fl_str_mv Discrete degree of symmetry of manifolds
title Discrete degree of symmetry of manifolds
spellingShingle Discrete degree of symmetry of manifolds
Mundet i Riera, Ignasi
Grups de transformacions
Topologia
Transformation groups
Topology
title_short Discrete degree of symmetry of manifolds
title_full Discrete degree of symmetry of manifolds
title_fullStr Discrete degree of symmetry of manifolds
title_full_unstemmed Discrete degree of symmetry of manifolds
title_sort Discrete degree of symmetry of 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 Grups de transformacions
Topologia
Transformation groups
Topology
topic Grups de transformacions
Topologia
Transformation groups
Topology
description We define the discrete degree of symmetry disc-sym $(X)$ of a closed $n$-manifold $X$ as the biggest $m \geq 0$ such that $X$ supports an effective action of $(\mathbb{Z} / r)^m$ for arbitrarily big values of $r$. We prove that if $X$ is connected then disc-sym $(X) \leq$ $3 n / 2$. We propose the question of whether for every closed connected $n$-manifold $X$ the inequality disc-sym $(X) \leq n$ holds true, and whether the only closed connected $n$-manifold $X$ for which disc-sym $(X)=n$ is the torus $T^n$. We prove partial results providing evidence for an affirmative answer to this question.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/216593
url https://hdl.handle.net/2445/216593
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/https://doi.org/10.1007/s00031-024-09858-z
Transformation Groups, 2024
https://doi.org/https://doi.org/10.1007/s00031-024-09858-z
dc.rights.none.fl_str_mv cc by (c) Ignasi Mundet i Riera, 2024
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by (c) Ignasi Mundet i Riera, 2024
http://creativecommons.org/licenses/by/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
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
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