Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Files

870730.pdf (823.69 KB)

Document type

Article

Version

Published version

Publication date

2024-04-19

Publication license

cc by (c) Ignasi Mundet i Riera, 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216593

Discrete degree of symmetry of manifolds

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

https://doi.org/https://doi.org/10.1007/s00031-024-09858-z

Abstract

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.

Subject

Grups de transformacions, Topologia

Subject (English)

Transformation groups, Topology

Citation

Collections

Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

MUNDET I RIERA, Ignasi. Discrete degree of symmetry of manifolds. Transformation Groups. 2024. ISSN 1083-4362. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/216593

Export metadata

JSON - METS

Share record