Topologically conjugate Kleinian groups

Author:
Ken'ichi Ohshika

Journal:
Proc. Amer. Math. Soc. **124** (1996), 739-743

MSC (1991):
Primary 30F40, 57M50

MathSciNet review:
1346983

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Abstract: Two Kleinian groups and are said to be topologically conjugate when there is a homeomorphism such that . It is conjectured that if two Kleinian groups and are topologically conjugate, one is a quasi-conformal deformation of the other. In this paper generalizing Minsky's result, we shall prove that this conjecture is true when is finitely generated and freely indecomposable, and the injectivity radii of all points of and are bounded below by a positive constant.

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Additional Information

**Ken'ichi Ohshika**

Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan

Email:
ohshika@math.titech.ac.jp

DOI:
http://dx.doi.org/10.1090/S0002-9939-96-03553-8

Keywords:
Kleinian group,
topological conjugacy

Received by editor(s):
November 17, 1993

Communicated by:
Ron Stern

Article copyright:
© Copyright 1996
American Mathematical Society