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

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

2005-01-20

arxiv.org/abs/math/0501316v2

Mathematics

Geometric Topology

22 pages, 10 figures: change of the title, and minor corrections

Scientific paper

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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