Dehn surgery and negatively curved 3-manifolds

Daryl Cooper; Marc Lackenby

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arXiv · math/9811082

Dehn surgery and negatively curved 3-manifolds

Daryl Cooper·Marc Lackenby

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Abstract

We show that, for any given 3-manifold M, there are at most finitely many hyperbolic knots K in the 3-sphere and fractions p/q (with q > 22), such that M is obtained by p/q surgery along K. This is a corollary of the following result. If M is obtained by Dehn filling the cusps of a hyperbolic 3-manifold X, where each filling slope has length more than 2 π+ ε, then, for any given M and ε> 0, there are only finitely many possibilities for X and for the filling slopes. In this paper, we also investigate the length of boundary slopes, and sequences of negatively curved metrics on a given 3-manifold.

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BibTeX RIS

Daryl Cooper, Marc Lackenby. 1998-11-12. Dehn surgery and negatively curved 3-manifolds. https://arxiv.org/abs/math/9811082

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