Parabolics on the boundary of the deformation space of a Kleinian group
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- by James W. Anderson PDF
- Proc. Amer. Math. Soc. 123 (1995), 589-591 Request permission
Abstract:
We present a condition on a loxodromic element L of a Kleinian group G which guarantees that L cannot be made parabolic on the boundary of the deformation space of G, namely, that the fixed points of L are separated by the limit set of a subgroup F of G which is a finitely generated quasifuchsian group of the first kind. The proof uses the collar theorem for short geodesics in hyperbolic 3-manifolds.References
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- Bernard Maskit, Kleinian groups, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 287, Springer-Verlag, Berlin, 1988. MR 959135
- Bernard Maskit, Parabolic elements in Kleinian groups, Ann. of Math. (2) 117 (1983), no. 3, 659–668. MR 701259, DOI 10.2307/2007038 K. Ohshika, Geometrically finite Kleinian groups and parabolic elements, preprint.
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 589-591
- MSC: Primary 30F40; Secondary 30F60, 57M50
- DOI: https://doi.org/10.1090/S0002-9939-1995-1223263-X
- MathSciNet review: 1223263