Covolumes of uniform lattices acting on polyhedral complexes

Details Covolumes of uniform lattices acting on polyhedral complexes Covolumes of uniform lattices acting on polyhedral complexes

2005-02-12

arxiv.org/abs/math/0502258v2

Mathematics

Group Theory

10 pages; main theorem extended to dimensions \geq 2; corollaries no longer require action without inversions

Scientific paper

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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