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arXiv · 1411.1105

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

Pierre Albin·Frédéric Rochon·David Sher
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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.

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Pierre Albin, Frédéric Rochon, David Sher. 2014-11-04. Analytic torsion and R-torsion of Witt representations on manifolds with cusps. https://doi.org/10.1215/00127094-2018-0009

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