On the Cohomology of Some Complex Hyperbolic Arithmetic 3-Manifolds

Abstract

Given an arithmetic lattice of the unitary group U(3,1) arising from a hermitian form over a CM-field, we show that all unitary representations of U(3,1) with nonzero cohomology contribute to the cohomology of the attached arithmetic complex 3-manifold, at least when we pass to a finite-index subgroup of the given arithmetic lattice.