arXiv 1205.11272012-05math.GRmath.NTmath.RA

双曲空间中的Poincaré平分线

Poincaré Bisectors in Hyperbolic Spaces

Eric Jespers, Stanley Orlando Juriaans, Ann Kiefer, Antonio Calixto de Souza Filho, Antonio De Andrade E Silva

备注：: This paper has been withdrawn by the authors because it was not very clear. We have splitted the results into two different papers making them clearer and better understandable. Those papers may be found on arxiv under the names "From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups" and "Dirichlet-Ford domains and Double Dirichlet domains"

摘要：

本文给出了在双曲二、三空间中构造Dirichlet基本区的平分线的显式公式。他们进行了比较，等距领域的建设中采用的福特域，并用于找到一个有限集的发电机的离散群体的有限covolume。应用于富克斯群、Kleinian群，包括Bianchi群，以及有限幂零群的整群环的单位群的生成元的有限集的构造。给出了一个易于实现的算法DAFC，并将其用于离散群生成元的搜索。

英文摘要：

We determine explicit formulas for the bisectors used in constructing a Dirichlet fundamental domain in hyperbolic two and three space. They are compared with the isometric spheres employed in the construction of a Ford domain and used to find a finite set of generators for discrete groups of finite covolume. Applications are given to Fuchsian groups, Kleinian groups, including the Bianchi groups, and for the construction of a finite set of generators of the unit group of the integral group ring of a finite nilpotent group. An easy implementable algorithm, DAFC, is also given and used in the search for generators of discrete groups.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文