ON THE GROWTH OF TORSION IN THE COHOMOLOGY OF SOME ARITHMETIC GROUPS OF Q-RANK ONE

Abstract Given a number field F with ring of integers O₅, one can associate to any torsion free subgroup of SL (2, O₅) of finite index a complete Riemannian manifold of finite volume with fibered cusp ends. For natural choices of flat vector bundles on such a manifold, we show that analytic torsion is identified with the Reidemeister torsion of the Borel-Serre compactification. This is used to obtain exponential growth of torsion in the cohomology for sequences of congruence subgroups.