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Bulletin of the London Mathematical Society Advance Access originally published online on December 15, 2006
Bulletin of the London Mathematical Society 2007 39(1):103-111; doi:10.1112/blms/bdl018
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© 2006 London Mathematical Society

Covolumes of uniform lattices acting on polyhedral complexes

Anne Thomas

Department of Mathematics
University of Chicago
Chicago, IL 60637
USA
athomas{at}math.uchicago.edu

Received 11 July 2005. Revision received 8 March 2006.

Let X be a polyhedral complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When X is two-dimensional and has all links isometric to either a complete bipartite graph or the building for a Chevalley group of rank 2 over a field of prime order, we obtain further restrictions on covolumes.


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