1998/11/12 by Daryl Cooper, Cooper, Daryl, Marc Lackenby +1 · 1 citation
Mathematics · #57M25 #57N10 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/9811082
35 pages, 2 figures. To be published in JDG
arxiv created 1998/11/12 · arxiv updated 2009/11/30
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.