Vanishing of $L^2$-cohomology and property (T) for groups acting on simplicial complexes

Details Vanishing of $L^2$-cohomology and property (T) for groups acting on simplicial complexes Vanishing of $L^2$-cohomology and property (T) for groups acting on simplicial complexes

2011-10-26

arxiv.org/abs/1110.5724v2

Mathematics

Group Theory

Scientific paper

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.

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