15 July 2018 Analytic torsion and R-torsion of Witt representations on manifolds with cusps
Pierre Albin, Frédéric Rochon, David Sher
Duke Math. J. 167(10): 1883-1950 (15 July 2018). DOI: 10.1215/00127094-2018-0009


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.


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Pierre Albin. Frédéric Rochon. David Sher. "Analytic torsion and R-torsion of Witt representations on manifolds with cusps." Duke Math. J. 167 (10) 1883 - 1950, 15 July 2018. https://doi.org/10.1215/00127094-2018-0009


Received: 22 January 2015; Revised: 10 August 2017; Published: 15 July 2018
First available in Project Euclid: 7 June 2018

zbMATH: 06928113
MathSciNet: MR3827813
Digital Object Identifier: 10.1215/00127094-2018-0009

Primary: 58J52
Secondary: 55N25 , 55N33 , 58J35 , 58J50

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

Rights: Copyright © 2018 Duke University Press


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Vol.167 • No. 10 • 15 July 2018
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