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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
  • Robert Brooks and J. Peter Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982), no. 1, 163–182. MR 650375
  • 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.
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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