On the growth of torsion in the cohomology of some arithmetic groups of ℚ-rank one

2024/01/25 by Mueller, Werner, Rochon, Frédéric
#53C35 #55N25 #58J52 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.14205

Abstract

Given a number field F with ring of integers O_F, one can associate to any torsion free subgroup of SL(2,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.

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