Annette Karrer (Ï㽶ÊÓƵ)
Title: The boundary rigidity of lattices in products of trees
Abstract: Each complete CAT(0) space has an associated topological space, called /visual boundary/ that coincides with the /Gromov boundary/ in case that the space is hyperbolic. A CAT(0) group $G$ is called /boundary rigid/ if the visual boundaries of all CAT(0) spaces admitting a geometric action by G are homeomorphic. If $G$ is hyperbolic, $G$ is boundary rigid. If G is not hyperbolic, G is not always boundary rigid. The first such example was found by Croke-Kleiner.
In this talk we will see that every torsion-free group acting geometrically a product of n regular trees of finite valence is boundary rigid. That means that every CAT(0) space that admits a geometric action of any such group has the boundary homeomorphic to a join of n copies of the Cantor set. This is joint work with Kasia Jankiewicz, Kim Ruane, and Bakul Sathaye.
We hope you all had an enjoyable summer and look forward to seeing everyone on Wednesday.