On finite simple and nonsolvable groups acting on homology 4-spheres |
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Authors: | Mattia Mecchia |
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Affiliation: | Università degli Studi di Trieste, Dipartimento di Matematica e Informatica, 34100 Trieste, Italy |
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Abstract: | The only finite non-Abelian simple group acting on a homology 3-sphere—necessarily non-freely—is the dodecahedral group A5≅PSL(2,5) (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group ). In the present paper we show that the only finite simple groups acting on a homology 4-sphere, and in particular on the 4-sphere, are the alternating or linear fractional groups A5≅PSL(2,5) and A6≅PSL(2,9). From this we deduce a short list of groups which contains all finite nonsolvable groups admitting an action on a homology 4-sphere. |
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Keywords: | 57M60 57S17 57S25 |
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