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On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one (2401.14205v1)
Published 25 Jan 2024 in math.DG, math.GT, and math.NT
Abstract: Given a number field $F$ with ring of integers $\mathcal{O}{F}$, one can associate to any torsion free subgroup of $\operatorname{SL}(2,\mathcal{O}{F})$ 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.