Algebraic and Geometric Topology 5 (2005), paper no. 21, pages 463-507.

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

Hiroshi Goda, Masakazu Teragaito

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

AMS subject classification. Primary: 57M25. Secondary: 57M50.

DOI: 10.2140/agt.2005.5.463

E-print: arXiv:math.GT/0501148

Submitted: 11 January 2005. (Revised: 13 April 2005.) Accepted: 29 April 2005. Published: 30 May 2005.

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Hiroshi Goda, Masakazu Teragaito
Department of Mathematics, Tokyo University of Agriculture and Technology
Koganei, Tokyo 184-8588, Japan
and
Department of Mathematics and Mathematics Education, Hiroshima University
1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
Email: goda@cc.tuat.ac.jp, teragai@hiroshima-u.ac.jp

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