The standard actions of finite groups on spheres are linear actions, or by finite subgroups of an orthogonal group. We prove that, in each dimension d > 5, there exists a finite group which admits a faithful, topological action on the sphere of dimension d but does not admit a faithful, linear actions, i.e. is not isomorphic to a finite subgroup of the orthogonal group O(d+1). The situation remains open for smooth actions.
Titolo: | On topological actions of finite, non-standard groups on spheres | |
Autori: | ||
Data di pubblicazione: | 2017 | |
Stato di pubblicazione: | Pubblicato | |
Rivista: | ||
Abstract: | The standard actions of finite groups on spheres are linear actions, or by finite subgroups of an orthogonal group. We prove that, in each dimension d > 5, there exists a finite group which admits a faithful, topological action on the sphere of dimension d but does not admit a faithful, linear actions, i.e. is not isomorphic to a finite subgroup of the orthogonal group O(d+1). The situation remains open for smooth actions. | |
Handle: | http://hdl.handle.net/11368/2921542 | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00605-016-0959-0 | |
URL: | https://link.springer.com/article/10.1007/s00605-016-0959-0 | |
Appare nelle tipologie: | 1.1 Articolo in Rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
pdf.pdf | Documento in Versione Editoriale | Copyright Editore | Administrator Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.