On the Cohomology of Some Complex Hyperbolic Arithmetic 3-Manifolds
Jian-Shu Li , Binyong Sun
Communications in Mathematics and Statistics ›› 2013, Vol. 1 ›› Issue (3) : 315 -329.
On the Cohomology of Some Complex Hyperbolic Arithmetic 3-Manifolds
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.
Cohomology / Unitary representation / Theta lift / Complex hyperbolic 3-manifold
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