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Hyperbolic tessellations associated to Bianchi groups

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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. © 2010 Springer-Verlag Berlin Heidelberg.

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Yasaki, D. (2010). Hyperbolic tessellations associated to Bianchi groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 385–396). https://doi.org/10.1007/978-3-642-14518-6_30

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