Topologically conjugate Kleinian groups
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- by Ken’ichi Ohshika PDF
- Proc. Amer. Math. Soc. 124 (1996), 739-743 Request permission
Abstract:
Two Kleinian groups $\Gamma _1$ and $\Gamma _2$ are said to be topologically conjugate when there is a homeomorphism $f:S^2 \rightarrow S^2$ such that $f \Gamma _1 f^{-1}= \Gamma _2$. It is conjectured that if two Kleinian groups $\Gamma _1$ and $\Gamma _2$ 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 $\Gamma _1$ is finitely generated and freely indecomposable, and the injectivity radii of all points of $\mathbf {H}^3/\Gamma _1$ and $\mathbf {H}^3/\Gamma _2$ are bounded below by a positive constant.References
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Additional Information
- Ken’ichi Ohshika
- Affiliation: Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152, Japan
- MR Author ID: 215829
- Email: ohshika@math.titech.ac.jp
- Received by editor(s): November 17, 1993
- Communicated by: Ron Stern
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 739-743
- MSC (1991): Primary 30F40, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-96-03553-8
- MathSciNet review: 1346983