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

Goda, Hiroshi; Teragaito, Masakazu

doi:10.2140/agt.2005.5.463

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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

DOI: 10.2140/agt.2005.5.463

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M50

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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

Volume 5, issue 2 (2005)