Thomas Haettel

Group actions on Helly graphs and injective metric spaces

We will survey recent results concerning group actions on injective metric spaces: those for which any family of pairwise intersecting balls has a non-empty global intersection. The discrete version is called a Helly graph. When a group acts nicely on such a space, one may deduce many properties typical of nonpositive curvature. We will present groups with such actions: hyperbolic groups, cocompact lattices in Lie groups, braid groups and Artin groups, mapping class groups of surfaces (joint with Nima Hoda and Harry Petyt).