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

2008/08/15 by Kai‐Uwe Bux, Bux, Kai-Uwe, Kevin Wortman +1
Engineering · #20E42 #20F65 #20G30 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Structural Analysis and Optimization

paper · pdf · doi:10.48550/arxiv.0808.2087

openalex publication_date 2008/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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