Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes

Abstract

We extend Ballmann and Swiatkowski's work on $L^2$-cohomology of groups acting on simplicial complexes and provide further vanishing results of $L^2$-cohomologies. In particular, we give a new criterion for property (T) for groups acting on an n-dimensional simplcial complex.

28 pages. few minor corrections from previous version

Cited by in corpus (2)

• Automorphism groups of simplicial complexes and rigidity for uniformly bounded representations
• Local spectral expansion approach to high dimensional expanders