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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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/216593 |
| Acesso em linha: | https://hdl.handle.net/2445/216593 |
| Access Level: | acceso abierto |
| Palavra-chave: | Grups de transformacions Topologia Transformation groups Topology |
| Resumo: | 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. |
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