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

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Let 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.
27 pages

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Group Theory, Geometric Topology, 20G30; 20E42; 20F65

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http://salesiana.dossiersoluciones.com/handle/123456789/167132

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.2087
 http://arxiv.org/abs/0808.2087

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arXiv