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Boundary Structure of Hyperbolic 3-Manifolds Admitting Annular and Toroidal Fillings at Large Distance

Published online by Cambridge University Press:  20 November 2018

Sangyop Lee  and
Masakazu Teragaito
Sangyop Lee
Affiliation:
Department of Mathematical Sciences, Seoul National University, San 56-1, Shinrim-dong, Kwanak-gu, Seoul 151-747, Korea e-mail: sangyop@snu.ac.kr
Masakazu Teragaito
Affiliation:
Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524 e-mail: teragai@hiroshima-u.ac.jp
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Abstract

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For a hyperbolic 3-manifold $M$ with a torus boundary component, all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such a situation, Gordon gave an upper bound of 5 for the distance between such slopes. Furthermore, the distance 4 is realized only by two specific manifolds, and 5 is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance 3. We show that if the distance is 3 then the boundary of the manifold consists of at most three tori.

Keywords

57M50Secondary57N10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 1 , 01 February 2008 , pp. 164 - 188
Copyright
Copyright © Canadian Mathematical Society 2008

References

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