Action dimension of lattices in Euclidean buildings

Schreve, Kevin

doi:10.2140/agt.2018.18.3257

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Action dimension of lattices in Euclidean buildings

Kevin Schreve

Algebraic & Geometric Topology 18 (2018) 3257–3277

DOI: 10.2140/agt.2018.18.3257

Abstract

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 $(2 n - 1)$ –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.

Keywords

action dimension, Euclidean building, S-arithmetic group, van Kampen obstruction

Mathematical Subject Classification 2010

Primary: 20F36, 20F65, 20F55, 57Q35

Secondary: 20J06

References

Publication

Received: 7 May 2017

Revised: 4 March 2018

Accepted: 17 April 2018

Published: 18 October 2018

Authors

Kevin Schreve
Department of Mathematics University of Michigan Ann Arbor, MI United States
https://sites.google.com/site/kevinschreve/

Volume 18, issue 6 (2018)