Commensurating actions and irreducible lattices

28 May 2013
Yves Cornulier
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.