Vanishing of cohomology and property (T) for groups acting on weighted   simplicial complexes
  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. 
Izhar Oppenheim
math.GR