On finite simple groups acting on homology spheres

Details On finite simple groups acting on homology spheres On finite simple groups acting on homology spheres

2011-06-06

arxiv.org/abs/1106.1067v2

Mathematics

Geometric Topology

13 pages; this is an extended and improved version which will appear in Monatshefte fuer Mathematik

Scientific paper

It is a consequence of the classical Jordan bound for finite subgroups of linear groups that in each dimension n there are only finitely many finite simple groups which admit a faithful, linear action on the n-sphere. In the present paper we prove an analogue for smooth actions on arbitrary homology n-spheres: in each dimension n there are only finitely many finite simple groups which admit a faithful, smooth action on some homology sphere of dimension n, and in particular on the n-sphere. We discuss also the finite simple groups which admit an action on a homology sphere of dimension 3, 4 or 5.

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