Volume 11, issue 2 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Infinite generation of non-cocompact lattices on right-angled buildings

Anne Thomas and Kevin Wortman

Algebraic & Geometric Topology 11 (2011) 929–938
Abstract

Let Γ be a non-cocompact lattice on a locally finite regular right-angled building X. We prove that if Γ has a strict fundamental domain then Γ is not finitely generated. We use the separation properties of subcomplexes of X called tree-walls.

Keywords
finite generation, lattice, building
Mathematical Subject Classification 2010
Primary: 20E42, 20F05
Secondary: 20F55, 57M07, 51E24
References
Publication
Received: 21 September 2010
Revised: 6 January 2011
Accepted: 18 January 2011
Published: 25 March 2011
Authors
Anne Thomas
School of Mathematics and Statistics
University of Sydney
Carslaw Building F07
Sydney NSW 2006
Australia
Kevin Wortman
Department of Mathematics
University of Utah
155 South 1400 East, Room 233
Salt Lake City UT 84112-0090
USA