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Hyperbolic Tessellations Associated to Bianchi Groups

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Algorithmic Number Theory (ANTS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6197))

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Abstract

Let F/ℚ be a number field. The space of positive definite binary Hermitian forms over F form an open cone in a real vector space. There is a natural decomposition of this cone into subcones. In the case of an imaginary quadratic field these subcones descend to hyperbolic space to give rise to tessellations of 3-dimensional hyperbolic space by ideal polytopes. We compute the structure of these polytopes for a range of imaginary quadratic fields.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, 27412, USA

    Dan Yasaki

Authors
  1. Dan Yasaki
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Editor information

Editors and Affiliations

  1. LIP/ENS-Lyon, 46, allée d’Italie, 69364, Lyon, Cedex 07, France

    Guillaume Hanrot

  2. Laboratoire d’Informatique (CNRS/UMR 7650), École polytechnique, 91128, Palaiseau Cedex, France

    François Morain

  3. INRIA Nancy, project CARAMEL, 615 rue du jardin botanique, 54602, Villers-lès-Nancy Cedex,, France

    Emmanuel Thomé

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Yasaki, D. (2010). Hyperbolic Tessellations Associated to Bianchi Groups. In: Hanrot, G., Morain, F., Thomé, E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14518-6_30

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  • DOI: https://doi.org/10.1007/978-3-642-14518-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14517-9

  • Online ISBN: 978-3-642-14518-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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