| Full text | |
| Author(s): |
Jespers, E.
;
Juriaans, S. O.
;
Kiefer, A.
;
e Silva, A. de A.
;
Souza Filho, A. C.
Total Authors: 5
|
| Document type: | Journal article |
| Source: | BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN; v. 23, n. 3, p. 465-479, JUL-SEP 2016. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 14/06325-1 - On the unit group of Z-orders in finite dimensional algebras |
| Grantee: | Antonio Calixto de Souza Filho |
| Support Opportunities: | Regular Research Grants |