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On volumes of quasi-arithmetic hyperbolic lattices

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Abstract

We prove that the covolume of any quasi-arithmetic hyperbolic lattice (a notion that generalizes the definition of arithmetic subgroups) is a rational multiple of the covolume of an arithmetic subgroup. As a corollary, we obtain a good description for the shape of the volumes of most of the known hyperbolic n-manifolds with \(n >3\).

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  1. Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Vincent Emery

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  1. Vincent Emery
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Correspondence to Vincent Emery.

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This work is supported by the Swiss National Science Foundation, Project number PP00P2_157583.

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Emery, V. On volumes of quasi-arithmetic hyperbolic lattices. Sel. Math. New Ser. 23, 2849–2862 (2017). https://doi.org/10.1007/s00029-017-0308-8

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