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2001 Kleinian groups with singly cusped parabolic fixed points
John R. Parker, Bernd O. Stratmann
Kodai Math. J. 24(2): 169-206 (2001). DOI: 10.2996/kmj/1106168782

Abstract

We consider geometrically infinite Kleinian groups and, in particular, groups with singly cusped parabolic fixed points. In order to distinguish between different geometric characteristics of such groups, we introduce the notion of horospherical tameness. We give a brief discussion of the fractal nature of their limit sets. Subsequently, we use Jørgensen's analysis of punctured torus groups to give a canonical decomposition into ideal tetrahedra of the geometrically infinite end. This enables us to relate horospherical tameness to Diophantine properties of Thurston's end invariants.

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John R. Parker. Bernd O. Stratmann. "Kleinian groups with singly cusped parabolic fixed points." Kodai Math. J. 24 (2) 169 - 206, 2001. https://doi.org/10.2996/kmj/1106168782

Information

Published: 2001
First available in Project Euclid: 19 January 2005

zbMATH: 1005.30030
MathSciNet: MR1839255
Digital Object Identifier: 10.2996/kmj/1106168782

Subjects:
Primary: 20H10
Secondary: 37F30

Rights: Copyright © 2001 Tokyo Institute of Technology, Department of Mathematics

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Vol.24 • No. 2 • 2001
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