On fundamental domains for subgroups of isometries acting in \(\mathbb H^n\)
type: Item
instance of: scholarly article
title: On fundamental domains for subgroups of isometries acting in \(\mathbb H^n\)
zbMATH Open document ID: 1250.30038
DOI: 10.5402/2012/685103
author: Antonio Lascurain Orive
author: Rubén Molina Hernández
published in: ISRN Geometry
publication date: 2012-09-07T00:00:00Z
review text: Summary: Given \(\mathcal P\), a fundamental polyhedron for the action of \(G\), a classical Kleinian group, acting in \(n\)-dimensional hyperbolic space, and \(\Gamma\), a finite index subgroup of \(G\), one obtains a fundamental domain for \(\Gamma\) pasting copies of \(\mathcal P\) 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 in \(\widehat{\mathbb R}^n\) is transitive on ``\(k\)-spheres''. Hence, we describe the hyperbolic \(k\)-planes in the upper half space model intrinsically, and provide 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.
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 6078640
zbMATH Keywords: Kleinian group
zbMATH Keywords: hyperbolic space
zbMATH Keywords: fundamental domain
Wikidata QID: Q58692108
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/685103
OpenAlex ID: W2062580468
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description: scientific article; zbMATH DE number 6078640