On finite simple and nonsolvable groups acting on closed 4-manifolds
| dc.creator | Mecchia, Mattia | |
| dc.creator | Zimmermann, Bruno | |
| dc.date | 2008-03-31 | |
| dc.date.accessioned | 2026-07-07T09:29:26Z | |
| dc.date.available | 2026-07-07T09:29:26Z | |
| dc.description | We show that the only finite nonabelian simple groups which admit a locally linear, homologically trivial action on a closed simply connected 4-manifold $M$ (or on a 4-manifold with trivial first homology) are the alternating groups $A_5$, $A_6$ and the linear fractional group PSL(2,7) (we note that for homologically nontrivial actions all finite groups occur). The situation depends strongly on the second Betti number $b_2(M)$ of $M$ and has been known before if $b_2(M)$ is different from two, so the main new result of the paper concerns the case $b_2(M)=2$. We prove that the only simple group that occurs in this case is $A_5$, and then give a short list of finite nonsolvable groups which contains all candidates for actions of such groups. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0803.4454 | |
| dc.identifier | http://arxiv.org/abs/0803.4454 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157785 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M60; 57S17; 57S25 | |
| dc.title | On finite simple and nonsolvable groups acting on closed 4-manifolds | |
| dc.type | text |