Analytic torsion and R-torsion of Witt representations on manifolds with cusps

Abstract

We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact hyperbolic spaces of finite volume, but we do not assume that the metric has constant curvature nor that the link of the cusp is a torus. We use renormalized traces in the sense of Melrose to define the analytic torsion and we relate it to the intersection R-torsion of Dar of the natural compactification to a stratified space. Our proof relies on our recent work on the behavior of the Hodge Laplacian spectrum on a closed manifold undergoing degeneration to a manifold with fibered cusps.

50 pages, 1 figure. v3: corrected typos and made changes to match with the new version of arXiv:1410.8406

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• Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps
• Sharp eigenvalue estimates on degenerating surfaces
• Resolvent, heat kernel and torsion under degeneration to fibered cusps
• Sub-Riemannian limit of the differential form heat kernels of contact manifolds
• Intersection torsion and analytic torsion of spaces with conical singularities
• Analytic torsion of finite volume hyperbolic orbifolds
• Analytic torsion for fibred boundary metrics and conic degeneration
• Asymptotics of automorphic spectra and the trace formula