Volume 5, issue 2 (2005)

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On hyperbolic 3–manifolds realizing the maximal distance between toroidal Dehn fillings

Hiroshi Goda and Masakazu Teragaito

Algebraic & Geometric Topology 5 (2005) 463–507
 arXiv: math.GT/0501148
Abstract

For a hyperbolic 3–manifold $M$ with a torus boundary component, all but finitely many Dehn fillings on the torus component yield hyperbolic 3–manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings, both of which yield toroidal manifolds. For such situation, Gordon gave an upper bound for the distance between two slopes of Dehn fillings. In particular, if $M$ is large, then the distance is at most 5. We show that this upper bound can be improved by 1 for a broad class of large manifolds.

Keywords
Dehn filling, toroidal filling, knot
Primary: 57M25
Secondary: 57M50
Publication
Received: 11 January 2005
Revised: 13 April 2005
Accepted: 29 April 2005
Published: 30 May 2005
Authors
 Hiroshi Goda Department of Mathematics Tokyo University of Agriculture and Technology Koganei Tokyo 184-8588 Japan Masakazu Teragaito Department of Mathematics and Mathematics Education Hiroshima University 1-1-1 Kagamiyama Higashi-hiroshima 739-8524 Japan