Dirichlet-Ford domains and Double Dirichlet domains

Autor(es)

Jespers, E. ; Juriaans, S. O. ; Kiefer, A. ; e Silva, A. de A. ; Souza Filho, A. C.

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN; v. 23, n. 3, p. 465-479, JUL-SEP 2016.
• Citações Web of Science: 0

Resumo

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 is an element of H-2 or center j is an element of H-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. (AU)

• Processo FAPESP: 14/06325-1 - Sobre o grupo de unidades de Z-ordens em álgebras de dimensão finita
• Beneficiário: Antonio Calixto de Souza Filho
• Modalidade de apoio: Auxílio à Pesquisa - Regular