Infinite generation of non-cocompact lattices on right-angled buildings

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.

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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

Volume 11, issue 2 (2011)

Anne Thomas and Kevin Wortman

Abstract