Duke Mathematical Journal

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

Pierre Albin, Frédéric Rochon, and David Sher

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We establish a Cheeger–Müller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all noncompact 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.

Article information

Duke Math. J., Volume 167, Number 10 (2018), 1883-1950.

Received: 22 January 2015
Revised: 10 August 2017
First available in Project Euclid: 7 June 2018

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Zentralblatt MATH identifier

Primary: 58J52: Determinants and determinant bundles, analytic torsion
Secondary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx] 58J35: Heat and other parabolic equation methods 55N25: Homology with local coefficients, equivariant cohomology 55N33: Intersection homology and cohomology

analytic torsion Reidemeister torsion locally symmetric spaces hyperbolic cusps analytic surgery determinant of the Laplacian


Albin, Pierre; Rochon, Frédéric; Sher, David. Analytic torsion and R-torsion of Witt representations on manifolds with cusps. Duke Math. J. 167 (2018), no. 10, 1883--1950. doi:10.1215/00127094-2018-0009. https://projecteuclid.org/euclid.dmj/1528358417

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