Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4252
Title: Finite Simple Groups Acting on 3-Manifolds and Homology Spheres
Authors: Reni, Marco
Zimmermann, Bruno
Issue Date: 2001
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: Marco Reni and Bruno Zimmermann, "Finite Simple Groups Acting on 3-Manifolds and Homology Spheres", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 32 (2001) suppl.1, pp. 305–315.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
32 suppl. 1 (2001)
Abstract: Any fi{}nite group admits actions on closed 3-manifolds, and in particular free actions. For actions with fi{}xed points, assumptions on the type of the fi{}xed point sets of elements drastically reduce the types of the possible groups. Concentrating on the basic case of fi{}nite simple groups we show in the present paper that, if some involution of a fi{}nite simple group G acting orientation-preservingly on a closed orientable 3-manifold has nonempty connected fi{}xed point set, then G is isomorphic to a projective linear group PSL(2, q), and thus of a very restricted type. The question was motivated by our work on the possible types of isometry groups of hyperbolic 3-manifolds occuring as cyclic branched coverings of knots in the 3-sphere. We characterize also fi{}nite groups which admit actions on $\mathbb{Z}_{2}$-homology spheres, generalizing corresponding results for integer homology spheres.
URI: http://hdl.handle.net/10077/4252
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.32 (2001) s1

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