Dirichlet-ford domains and double Diriohlet domains

We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic 2- and 3-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains a...

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Bibliographic Details
Published in:Bulletin of the Belgian Mathematical Society, Simon Stevin Simon Stevin, 2016-07, Vol.23 (3), p.465
Main Authors: Jespers, E, Juriaans, S.O, Kiefer, A, de A. e Silva, A, Filho, A.C. Souza
Format: Article
Language:English
Subjects:
Groups (Mathematics)
Mathematical research
Topological spaces
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Summary:We continue investigations started by Lakeland on Fuchsian and Kleinian groups which have a Dirichlet fundamental domain that also is a Ford domain in the upper half-space model of hyperbolic 2- and 3-space, or which have a Dirichlet domain with multiple centers. Such domains are called DF-domains and Double Dirichlet domains respectively. Making use of earlier obtained concrete formulas for the bisectors defining the Dirichlet domain of center i [member of] [H.sup.2] or center j [member of] [H.sup.3], we obtain a simple condition on the matrix entries of the side-pairing transformations of the fundamental domain of a Fuchsian or Kleinian group to be a DF-domain. Using the same methods, we also complement a result of Lakeland stating that a cofinite Fuchsian group has a DF domain (or a Dirichlet domain with multiple centers) if and only if it is an index 2 subgroup of the discrete group G of reflections in a hyperbolic polygon. Key words and phrases: Hyperbolic space, Kleinian groups, Fundamental domains.
ISSN:1370-1444