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Hyperbolic tessellations associated to Bianchi groups

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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.




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).

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