Irreducible lattices, invariant means, and commensurating actions

Abstract

We study rigidity properties of lattices in terms of invariant means and commensurating actions (or actions on CAT(0) cube complexes). We notably study Property FM for groups, namely that any action on a discrete set with an invariant mean has a finite orbit.

31 pages, 0 figure

Cited by in corpus (7)

• The Median Class and Superrigidity of Actions on CAT(0) Cube Complexes
• Roller boundaries for median spaces and algebras
• Commensurating actions for groups of piecewise continuous transformations
• Commensurating actions of birational groups and groups of pseudo-automorphisms
• A note on locally elliptic actions on cube complexes
• Property FW, differentiable structures, and smoothability of singular actions
• A quantitative Neumann lemma for finitely generated groups