Geodesic
On hyperbolic 3–manifolds realizing the maximal distance between toroidal Dehn fillings
Goda, Hiroshi1 ; Teragaito, Masakazu2
1Department of Mathematics, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan
2Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima 739-8524, Japan
Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 463-507
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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.

DOI : 10.2140/agt.2005.5.463
Keywords: Dehn filling, toroidal filling, knot

Goda, Hiroshi  1   ; Teragaito, Masakazu  2

1 Department of Mathematics, Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan
2 Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima 739-8524, Japan 
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Goda, Hiroshi; Teragaito, Masakazu. On hyperbolic 3–manifolds realizing the maximal distance between toroidal Dehn fillings. Algebraic and Geometric Topology, Tome 5 (2005) no. 2, pp. 463-507. doi: 10.2140/agt.2005.5.463

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