On finite simple and nonsolvable groups acting on homology 4-spheres
| dc.creator | Mecchia, Mattia | |
| dc.creator | Zimmermann, Bruno | |
| dc.date | 2005-07-08 | |
| dc.date.accessioned | 2026-07-07T08:38:12Z | |
| dc.date.available | 2026-07-07T08:38:12Z | |
| dc.description | The only finite nonabelian simple group acting on a homology 3-sphere - necessarily non-freely - is the dodecahedral group $\Bbb A_5 \cong {\rm PSL}(2,5)$ (in analogy, the only finite perfect group acting freely on a homology 3-sphere is the binary dodecahedral group $\Bbb A_5^* \cong {\rm SL}(2,5)$). 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 groups $\Bbb A_5 \cong {\rm PSL}(2,5)$ and $\Bbb A_6 \cong {\rm PSL}(2,9)$. From this we deduce a short list of groups which contains all finite nonsolvable groups admitting an action on a homology 4-spheres. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0507173 | |
| dc.identifier | http://arxiv.org/abs/math/0507173 | |
| dc.identifier | Topology Appl. 153 (2006), 2933-2942. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140641 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M60; 57S17; 57S25 | |
| dc.title | On finite simple and nonsolvable groups acting on homology 4-spheres | |
| dc.type | text |