L^2-Betti numbers of one-relator groups
| dc.creator | Dicks, Warren | |
| dc.creator | Linnell, Peter A. | |
| dc.date | 2005-08-19 | |
| dc.date | 2006-09-19 | |
| dc.date.accessioned | 2026-07-07T08:07:11Z | |
| dc.date.available | 2026-07-07T08:07:11Z | |
| dc.description | We determine the L^2-Betti numbers of all one-relator groups and all surface-plus-one-relation groups (surface-plus-one-relation groups were introduced by Hempel who called them one-relator surface groups). In particular we show that for all such groups G, the L^2-Betti numbers b_n^{(2)}(G) are 0 for all n>1. We also obtain some information about the L^2-cohomology of left-orderable groups, and deduce the non-L^2 result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. | |
| dc.description | 18 pages, version 3, minor changes. To appear in Math. Ann | |
| dc.identifier | https://arxiv.org/abs/math/0508370 | |
| dc.identifier | http://arxiv.org/abs/math/0508370 | |
| dc.identifier | Math. Ann. 337 (2007), no. 4, 855-874 | |
| dc.identifier | doi:10.1007/s00208-006-0058-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130856 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F05, (Primary) 16S34, 20J05 (Secondary) | |
| dc.title | L^2-Betti numbers of one-relator groups | |
| dc.type | text |