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

Mattia Mecchia; Bruno Zimmermann

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arXiv · 1001.3976

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

Mattia Mecchia·Bruno Zimmermann

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Abstract

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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BibTeX RIS

Mattia Mecchia, Bruno Zimmermann. 2010-04-13. On finite groups acting on homology 4-spheres and finite subgroups of SO(5). https://arxiv.org/abs/1001.3976

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