Volume 18, issue 6 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 7, 3217–3753
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Action dimension of lattices in Euclidean buildings

Kevin Schreve

Algebraic & Geometric Topology 18 (2018) 3257–3277
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 (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.

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/