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Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds

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Abstract

For \(d=2n+1\) a positive odd integer, we consider sequences of arithmetic subgroups of \({\text {SO}}_0(d,1)\) and yielding corresponding hyperbolic manifolds of finite volume and show that, under appropriate and natural assumptions, the torsion of the associated cohomology groups grows exponentially.

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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, Montreal, 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. Exponential growth of torsion in the cohomology of arithmetic hyperbolic manifolds. Math. Z. 298, 79–106 (2021). https://doi.org/10.1007/s00209-020-02587-5

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