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.
On topological actions of finite, non-standard groups on spheres
Zimmermann Bruno
2017
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.File in questo prodotto:
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