Invariant currents and automorphic forms of an elementary Kleinian group

Abstract

We compute the cohomology of currents invariant by some elementary Kleinian groups. The result is used to compute the cohomology of harmonic coclosed automorphic forms on the hyperbolic space of even dimension for such a group. This proves that for these groups the cohomology of these forms is isomorphic to the cohomol- ogy of the quotient space. This question is related to the Borel conjecture ( cf. Corollaries 2.14 and 3.9).