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FROM GEOMETRY TO ARITHMETIC OF COMPACT HYPERBOLIC COXETER POLYTOPES

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Abstract

We establish some geometric constraints on compact Coxeter polytopes in hyperbolic spaces and show that these constraints can be a very useful tool for the classification problem of reflective anisotropic Lorentzian lattices and cocompact arithmetic hyperbolic reflection groups.

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Authors and Affiliations

  1. The Kharkevich Institute for Information Transmission Problems, Moscow, Russia

    NIKOLAY BOGACHEV

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    NIKOLAY BOGACHEV

  3. Skolkovo Institute of Science and Technology, Skolkovo, Russia

    NIKOLAY BOGACHEV

  4. Caucasus Mathematical Center, Adyghe State University, Maikop, Russia

    NIKOLAY BOGACHEV

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Dedicated to the memory of Èrnest Borisovich Vinberg (1937–2020)

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This work was supported by the RFBR grant 18-31-00427. A software implementation VinAl [9] used in this paper for testing a reflectivity of candidate-lattices (see Section 7) was supported by the Russian Science Foundation (Project no. 18-71-00153).

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BOGACHEV, N. FROM GEOMETRY TO ARITHMETIC OF COMPACT HYPERBOLIC COXETER POLYTOPES. Transformation Groups 28, 77–105 (2023). https://doi.org/10.1007/s00031-022-09747-3

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