GGT Seminar: Annette Karrer (Technion): The rigidity of lattices in products of trees
Thursday, 14.10.2021 15:00 im Raum SRZ 216/217
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 group acting freely and cocompactly on a product of two 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 two copies of the Cantor set. The proof of this result uses a generalization of classical dynamics on boundaries introduced by Guralnik and Swenson. I will explain the idea of this generalization by explaining a higher-dimensional version of classical North-south-dynamics obtained this way.
Joint work with Kasia Jankiewicz, Kim Ruane, and Bakul Sathaye.