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Proceedings of the American Mathematical Society

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

 

 

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
MathSciNet review: 1223263
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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.


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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