Volume 18, issue 6 (2018)

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Action dimension of lattices in Euclidean buildings

Kevin Schreve

Algebraic & Geometric Topology 18 (2018) 3257–3277

We show that if a discrete group Γ acts properly and cocompactly on an n–dimensional, thick, Euclidean building, then Γ cannot act properly on a contractible (2n1)–manifold. As an application, if Γ is a torsion-free S–arithmetic group over a number field, we compute the minimal dimension of contractible manifold that admits a proper Γ–action. This partially answers a question of Bestvina, Kapovich, and Kleiner.

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action dimension, Euclidean building, S-arithmetic group, van Kampen obstruction
Mathematical Subject Classification 2010
Primary: 20F36, 20F65, 20F55, 57Q35
Secondary: 20J06
Received: 7 May 2017
Revised: 4 March 2018
Accepted: 17 April 2018
Published: 18 October 2018
Kevin Schreve
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States