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

References in corpus (7)

• A torsion Jacquet--Langlands correspondence
• Torsion homology growth and cycle complexity of arithmetic manifolds
• A gluing formula for the analytic torsion on hyperbolic manifolds with cusps
• Resolution of the canonical fiber metrics for a Lefschetz fibration
• Cheeger-Mueller Theorem on manifolds with cusps
• The Intersection R-Torsion for Finite Cone
• Resolvent, heat kernel and torsion under degeneration to fibered cusps

Cited by in corpus (11)

• The heat kernel on curvilinear polygonal domains in surfaces
• A Cheeger-Müller theorem for manifolds with wedge singularities
• Cheeger-Mueller Theorem on manifolds with cusps
• 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