The derived series and virtual Betti numbers
| dc.creator | Gadgil, Siddhartha | |
| dc.date | 2003-06-25 | |
| dc.date.accessioned | 2026-07-07T04:59:10Z | |
| dc.date.available | 2026-07-07T04:59:10Z | |
| dc.description | The virtual Betti number conjecture states that any hyperbolic three-manifold has a finite cover with positive first Betti number. We show that this would follow if it were known that the derived series of the fundamental group $G$ of a hyperbolic three-manifold satisfies a certain stability property. The stability property is the statement that if all the quotients $G^i/G^{i+1}$ of the derived series $G^i$ of $G$ are finite, then the derived series stabilises. The proof involves basic facts regarding finite group actions on homology spheres. | |
| dc.description | 2 pages | |
| dc.identifier | https://arxiv.org/abs/math/0306359 | |
| dc.identifier | http://arxiv.org/abs/math/0306359 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67876 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M05; 57M10 ; 57M60 | |
| dc.title | The derived series and virtual Betti numbers | |
| dc.type | text |