Kodai Mathematical Journal

Kleinian groups with singly cusped parabolic fixed points

John R. Parker and Bernd O. Stratmann

Full-text: Open access

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.

Article information

Source
Kodai Math. J. Volume 24, Number 2 (2001), 169-206.

Dates
First available in Project Euclid: 19 January 2005

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1106168782

Digital Object Identifier
doi:10.2996/kmj/1106168782

Mathematical Reviews number (MathSciNet)
MR1839255

Zentralblatt MATH identifier
1005.30030

Subjects
Primary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Secondary: 37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems

Citation

Parker, John R.; Stratmann, Bernd O. Kleinian groups with singly cusped parabolic fixed points. Kodai Math. J. 24 (2001), no. 2, 169--206. doi:10.2996/kmj/1106168782. http://projecteuclid.org/euclid.kmj/1106168782.


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