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

摘要

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