Geodesic
Boundary Structure of Hyperbolic 3-Manifolds Admitting Annular and Toroidal Fillings at Large Distance
Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 164-188

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2008-007-6
Mots-clés : 57M50, Secondary, 57N10 
Lee, Sangyop; Teragaito, Masakazu. Boundary Structure of Hyperbolic 3-Manifolds Admitting Annular and Toroidal Fillings at Large Distance. Canadian journal of mathematics, Tome 60 (2008) no. 1, pp. 164-188. doi: 10.4153/CJM-2008-007-6
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