Abstract

Let M be a hyperbolizable 3-manifold with nonempty incompressible boundary of negative Euler characteristic. Suppose that B1,..., Bk is a collection of components of the interior of the space of complete, marked hyperbolic 3-manifolds homotopy equivalent to M, such that for any i, j, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. We prove that there is a geometrically finite hyperbolic structure on int(M) which is in the closure of each Bi. Moreover, we show that this structure can be constructed so as to admit quasiconformal deformations which also lie in the closure of every Bi.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 691-736
Launched on MUSE
2003-07-08
Open Access
No
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