Connectivity Properties of Horospheres in Euclidean Buildings and Applications to Finiteness Properties of Discrete Groups

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dc.creatorBux, Kai-Uwe
dc.creatorWortman, Kevin
dc.date2008-08-15
dc.date.accessioned2026-07-07T09:56:52Z
dc.date.available2026-07-07T09:56:52Z
dc.descriptionLet G(O_S) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O_S) established in an earlier paper is sharp in this case. The geometric analysis underlying our result determines the conectivity properties of horospheres in thick Euclidean buildings.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/0808.2087
dc.identifierhttp://arxiv.org/abs/0808.2087
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167132
dc.subjectGroup Theory
dc.subjectGeometric Topology
dc.subject20G30; 20E42; 20F65
dc.titleConnectivity Properties of Horospheres in Euclidean Buildings and Applications to Finiteness Properties of Discrete Groups
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