Dehn surgery and negatively curved 3-manifolds

Journal article

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 \pi + \epsilon, then, for any given M and \epsilon > 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.

Authors: Cooper, D; Lackenby, M

• Publication status: Published
• Journal: JOURNAL OF DIFFERENTIAL GEOMETRY
• Volume: 50
• Issue: 3
• Pages: 591-624
• Publication date: 1998-11-12
• ISSN: 0022-040X
• Language: English
• Keywords: 57N10, 57M25; math.GT