Superrigidity of actions on finite rank median spaces

Vortrag von Elia Fioravanti

Sprecher eingeladen von: Prof. Dr. Viktor Schroeder

Datum: 25.04.18  Zeit: 15.45 - 18.00  Raum: ETH HG G 43

Finite rank median spaces simultaneously generalise real trees and finite dimensional CAT(0) cube complexes. Requiring a group to act on a finite rank median space is in general much more restrictive than only asking for an action on a general median space. This is particularly evident for certain irreducible lattices in products of rank-one simple Lie groups: they admit proper cocompact actions on infinite rank median spaces, but any action on a (connected) finite rank median space must fix a point. Our proof of the latter fact is based on a generalisation of a superrigidity result of Chatterji-Fernos-Iozzi. We will sketch the necessary techniques, focussing on differences between cube complexes and general median spaces. We will also discuss applications of the fixed-point property to a large family of coarse median groups, which includes all hierarchically hyperbolic groups.