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Parabolics on the boundary of the deformation space of a Kleinian group


Author: James W. Anderson
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
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] R. Brooks and J. Matelski, Collars in Kleinian groups, Duke Math. J. 49 (1982), 163-182. MR 650375 (83f:30039)
  • [2] B. Maskit, Kleinian groups, Springer-Verlag, New York, 1988. MR 959135 (90a:30132)
  • [3] -, Parabolic elements in Kleinian groups, Ann. of Math. (2) 117 (1983), 659-668. MR 701259 (85a:30073)
  • [4] K. Ohshika, Geometrically finite Kleinian groups and parabolic elements, preprint.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1223263-X
Keywords: Parabolic element, deformation space, collar theorem
Article copyright: © Copyright 1995 American Mathematical Society

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