A torsion correspondence for non-compact arithmetic hyperbolic 3-manifolds

Abstract

The Cheeger-Müller theorem (formerly Ray-Singer conjecture) is one of the seminal results for closed orientable Riemannian manifolds. It implies that for a compact hyperbolic 3−manifold, the analytic torsion and Reidemeister torsion coincide. An analogous result does not exist for non-compact hyperbolic 3−manifolds. We explore a result that compares non-compact these torsions in arithmetic manifolds of a special kind.