Volume 5, issue 2 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M50
References
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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