#### 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.

Notes on file formats
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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