Algebraic & Geometric Topology

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

Hiroshi Goda and Masakazu Teragaito

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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

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

Received: 11 January 2005
Revised: 13 April 2005
Accepted: 29 April 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M50: Geometric structures on low-dimensional manifolds

Dehn filling toroidal filling knot


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.

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