A Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory

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dc.creatorBell, G. C.
dc.creatorDranishnikov, A. N.
dc.date2004-07-25
dc.date.accessioned2026-07-07T05:10:40Z
dc.date.available2026-07-07T05:10:40Z
dc.descriptionWe prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpoltent and polycyclic groups in terms of their Hirsch length. We are also able to improve the known upper bounds on the asymptotic dimension of fundamental groups of complexes of groups, amalgamated free products and the hyperbolization of metric spaces possessing the Higson property.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0407431
dc.identifierhttp://arxiv.org/abs/math/0407431
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72000
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20F69, 20F65
dc.titleA Hurewicz-type theorem for asymptotic dimension and applications to geometric group theory
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