L^2-Betti numbers of one-relator groups

dc.creatorDicks, Warren
dc.creatorLinnell, Peter A.
dc.date2005-08-19
dc.date2006-09-19
dc.date.accessioned2026-07-07T08:07:11Z
dc.date.available2026-07-07T08:07:11Z
dc.descriptionWe 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.description18 pages, version 3, minor changes. To appear in Math. Ann
dc.identifierhttps://arxiv.org/abs/math/0508370
dc.identifierhttp://arxiv.org/abs/math/0508370
dc.identifierMath. Ann. 337 (2007), no. 4, 855-874
dc.identifierdoi:10.1007/s00208-006-0058-y
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130856
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F05, (Primary) 16S34, 20J05 (Secondary)
dc.titleL^2-Betti numbers of one-relator groups
dc.typetext

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