The Baum-Connes conjecture and proper group actions on affine buildings

Simple item page
dc.creatorMatsnev, Dmitry
dc.date2007-03-30
dc.date.accessioned2026-07-07T07:55:07Z
dc.date.available2026-07-07T07:55:07Z
dc.descriptionWe study the possibility of applying a finite-dimensionality argument in order to address parts of the Baum-Connes conjecture for finitely generated linear groups. This gives an alternative approach to the results of Guentner, Higson, and Weinberger concerning the Baum-Connes conjecture for linear groups. For any finitely generated linear group over a field of characteristic zero we construct a proper action on a finite-asymptotic-dimensional CAT(0)-space, provided that for such a group its unipotent subgroups have `bounded composition rank'. The CAT(0)-space in our construction is a finite product of symmetric spaces and affine Bruhat-Tits buildings. For the case of finitely generated subgroup of SL(2,C) the result is sharpened to show that the Baum-Connes assembly map is an isomorphism.
dc.identifierhttps://arxiv.org/abs/math/0703923
dc.identifierhttp://arxiv.org/abs/math/0703923
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126860
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subjectMetric Geometry
dc.subject20F65; 20G15; 51K05
dc.titleThe Baum-Connes conjecture and proper group actions on affine buildings
dc.typetext

Files

Collections

arXiv