, Volume 7, Issue 4, pp 615-645

On L2-cohomology and Property (T) for Automorphism Groups of Polyhedral Cell Complexes

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We present an update of Garland's work on the cohomology of certain groups, construct a class of groups many of which satisfy Kazhdan's Property (T) and show that properly discontinuous and cocompact groups of automorphisms of (4,4) or (6,3)-complexes do not satisfy Property (T).

Submitted: September 1996, final version: March 1997