Kodai Mathematical Journal

Kleinian groups with singly cusped parabolic fixed points

John R. Parker and Bernd O. Stratmann

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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

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

First available in Project Euclid: 19 January 2005

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Zentralblatt MATH identifier

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


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. https://projecteuclid.org/euclid.kmj/1106168782

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