Lattices in automorphism groups of right-angled buildings

Anne Thomas (Cornell)

Wednesday 15th October, 2008 16:00-17:00 214


We compare several properties of lattices in semisimple Lie groups (the classical setting) with lattices in $G$ the automorphism group of a right-angled building. Examples of right-angled buildings include products of trees, and some hyperbolic buildings which, by work of Bourdon-Pajot, have rigidity properties similar to the classical setting. We show that, in contrast, lattices in $G$ share much of the flexibility of lattices acting on trees. For instance, every positive real number is the covolume of uncountably many lattices in $G$. We also describe recent joint work with Angela Kubena Barnhill, showing that in many cases every uniform lattice $\Gamma$ has dense commensurator in $G$.

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