Two approaches towards property (T) for groups acting on simplicial complexes

TL;DR

This paper extends two methods for establishing property (T) in groups acting on simplicial complexes, providing new criteria for property (T) and vanishing higher L2-cohomologies.

Contribution

It generalizes Zuk's criterion and Kassabov's work to develop new criteria for property (T) in this context.

Findings

New criteria for property (T)

Criteria for vanishing higher L2-cohomologies

Generalizations of existing approaches

Abstract

This article generalizes two approaches for property (T) - the first is a generalization of Zuk's criterion for property (T) and the second is a generalization of the work of Kassabov regarding property (T) and subspace arrangements. In both cases we obtain new criteria for property (T) (and for vanishing of higher L2-cohomologies).