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Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps

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Abstract

On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel–Serre compactification of the manifold. In a companion paper, this formula is used to derive exponential growth of torsion in cohomology of arithmetic groups.

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Notes

  1. Since \(\frac{x}{\rho }=\sin \theta \) in the coordinates of [ARS14].

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Acknowledgements

The authors are grateful to the hospitality of the Centre International de Rencontres Mathématiques (CIRM) where this project started. The second author was supported by NSERC and a Canada Research Chair.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Endnicher Allee 60, 53115, Bonn, Germany

    Werner Müller

  2. Département de Mathématiques, UQÀM, C.P. 8888, Succ. Centre-Ville, Montreal, QC, H3C 3P8, Canada

    Frédéric Rochon

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  1. Werner Müller
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  2. Frédéric Rochon
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Correspondence to Frédéric Rochon.

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Müller, W., Rochon, F. Analytic torsion and Reidemeister torsion of hyperbolic manifolds with cusps. Geom. Funct. Anal. 30, 910–954 (2020). https://doi.org/10.1007/s00039-020-00536-2

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