On Fundamental Domains for Subgroups of Isometries Acting in ℍn. (11th July 2012)

• Record Type: Journal Article
• Authors: Lascurain Orive, Antonio; Molina Hernández, Rubén
• Other Names: Fino A. Academic Editor.; Saidi E. H. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2012(2012)
• Publication Date: 2012-07-11
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.5402/2012/685103
• Languages: English
• ISSNs: 2090-6307

Abstract

Abstract : Given𝒫 a fundamental polyhedron for the action ofG, a classical kleinian group, acting inn -dimensional hyperbolic space, andΓ, a finite index subgroup ofG, one obtains a fundamental domain forΓ pasting copies of𝒫 by a Schreier process. It also generalizes the side pairing generating theorem for exact or inexact polyhedra. It is proved as well that the general Möbius group acting inℝ ^ n is transitive on "k -spheres". Hence, describing the hyperbolick -planes in the upper half space model intrinsically, and providing also an alternative proof of the transitive action on them. Some examples are given in detail, derived from the classical modular group and the Picard group.