Boundary structures of hyperbolic 3-manifolds admitting annular and toroidal fillings at large distance

Sangyop Lee; Masakazu Teragaito

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arXiv · math/0501316

Boundary structures of hyperbolic 3-manifolds admitting annular and toroidal fillings at large distance

Sangyop Lee·Masakazu Teragaito

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Abstract

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 situation, Gordon gave an upper bound 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 three then the boundary of the manifold consists of at most three tori.

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BibTeX RIS

Sangyop Lee, Masakazu Teragaito. 2005-03-01. Boundary structures of hyperbolic 3-manifolds admitting annular and toroidal fillings at large distance. https://arxiv.org/abs/math/0501316

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