Title: Hyperbolic rigidity of higher rank lattices
Speaker: Thomas Haettel (Montpellier)
Abstract: Higher rank lattices, like $$SL(n,Z) for \(n$$ at least 3, enjoy numerous rigidity properties: every isometric action on a tree or on a Hilbert space has a fixed point, for instance. We will show that every action by isometries of a higher rank lattice on a Gromov-hyperbolic space is elementary. Among consequences, we obtain another proof of the Farb-Kaimanovich-Masur Theorem that any morphism from a higher rank lattice to a mapping class group has finite image. Guirardel and Horbez also deduce another proof of the Bridson-Wade theorem that any morphism from a higher rank lattice to $$\mathrm{Out}(F_n)$$ has finite image.