On finite groups acting on homology 4-spheres and finite subgroups of SO(5)

Details On finite groups acting on homology 4-spheres and finite subgroups of SO(5) On finite groups acting on homology 4-spheres and finite subgroups of SO(5)

2010-01-22

arxiv.org/abs/1001.3976v2

Mathematics

Geometric Topology

13 pages

Scientific paper

We show that a finite group which admits a faithful, smooth, orientation-preserving action on a homology 4-sphere, and in particular on the 4-sphere, is isomorphic to a subgroup of the orthogonal group SO(5), by explicitly determining the various groups which can occur (up to an indetermination of index two in the case of solvable groups). As a consequence we obtain also a characterization of the finite groups which are isomorphic to subgroups of the orthogonal groups SO(5) and O(5).

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