On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one

Abstract

Given a number field $F$ with ring of integers ${\mathcal{O}}_F$, one can associate to any torsion free subgroup of $\mathrm{SL}(2,{\mathcal{O}}_F)$ 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.

arXiv commentminor corrections, final version, 46 pages