Groups, Geometry, and Dynamics


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Volume 9, Issue 1, 2015, pp. 67–101
DOI: 10.4171/GGD/306

Published online: 2015-04-28

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

Izhar Oppenheim[1]

(1) Ben Gurion University of the Negev, Beer Sheva, Israel

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

Keywords: Kazhdan property (T), graph Laplacian, continuous cohomology, simplicial complexes, Garland’s method

Oppenheim Izhar: Vanishing of cohomology and property (T) for groups acting on weighted simplicial complexes. Groups Geom. Dyn. 9 (2015), 67-101. doi: 10.4171/GGD/306