## Algebraic & Geometric Topology

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

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 5, Number 2 (2005), 463-507.

Dates
Revised: 13 April 2005
Accepted: 29 April 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796419

Digital Object Identifier
doi:10.2140/agt.2005.5.463

Mathematical Reviews number (MathSciNet)
MR2153119

Zentralblatt MATH identifier
1082.57011

Keywords
Dehn filling toroidal filling knot

#### Citation

Goda, Hiroshi; Teragaito, Masakazu. On hyperbolic 3–manifolds realizing the maximal distance between toroidal Dehn fillings. Algebr. Geom. Topol. 5 (2005), no. 2, 463--507. doi:10.2140/agt.2005.5.463. https://projecteuclid.org/euclid.agt/1513796419

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