Hyperbolic Tessellations Associated to Bianchi Groups

  • Dan Yasaki
Conference paper

DOI: 10.1007/978-3-642-14518-6_30

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dan Yasaki
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of North Carolina at GreensboroGreensboroUSA

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