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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| 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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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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article |
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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 |
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cc by (c) Ignasi Mundet i Riera, 2024 http://creativecommons.org/licenses/by/3.0/es/ |
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openAccess |
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application/pdf |
| dc.publisher.none.fl_str_mv |
Springer Verlag |
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Springer Verlag |
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Articles publicats en revistes (Matemàtiques i Informàtica) reponame:Dipòsit Digital de la UB instname:Universidad de Barcelona |
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Universidad de Barcelona |
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Dipòsit Digital de la UB |
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Dipòsit Digital de la UB |
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15,811543 |