Volume 12 (2007)

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Kleinian orbifolds uniformized by RP groups with an elliptic and a hyperbolic generator

Elena Klimenko and Natalia Kopteva

Geometry & Topology Monographs 12 (2007) 121–156

DOI: 10.2140/gtm.2007.12.121

arXiv: 0903.5472

Abstract

We consider non-elementary Kleinian groups Γ without invariant plane generated by an elliptic and a hyperbolic elements with their axes lying in one plane. We find presentations and a complete list of orbifolds uniformized by such Γ.

Keywords

Kleinian group, discrete group, hyperbolic geometry, hyperbolic orbifold

Mathematical Subject Classification

Primary: 30F40

Secondary: 22E40, 57M12, 57M50

References
Publication

Received: 6 October 2006
Revised: 16 March 2007
Accepted: 30 April 2007
Published: 3 December 2007

Authors
Elena Klimenko
Max Planck Institute for Mathematics
Vivatsgasse 7
53111 Bonn
Germany
Natalia Kopteva
Sobolev Institute of Mathematics
Acad. Koptyug ave., 4
Novosibirsk 630090
Russia