Commensurating actions and irreducible lattices

28 May 2013
17:00
Yves Cornulier
Abstract
We will first recall the known notion of commensurating actions and its link to actions on CAT(0) cube complexes. We define a group to have Property FW if every isometric action on a CAT(0) cube complex has a fixed point. We conjecture that every irreducible lattice in a semisimple Lie group of higher rank has Property FW, and will give some instances beyond the trivial case of Kazhdan groups.