### Boundary rigidity of groups acting on products of trees

Algebra Seminar

9th March 2022, 2:30 pm – 3:30 pm

Fry Building, Room G.11 and Zoom

Each complete CAT(0) space has an associated topological space, called the visual boundary. 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. Hyperbolic groups are boundary rigid. However, if G is not hyperbolic, G might not be boundary rigid, as demonstrated by examples by Croke-Kleiner. We show that groups acting geometrically on a product of two trees are boundary rigid. In particular, every CAT(0) space that admits a geometric action of such a group has boundary homeomorphic to a join of two Cantor sets. This is joint work with Jankiewicz, Karrer, and Ruane.

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