Toroidal Dehn fillings on large hyperbolic 3-manifolds

Details Toroidal Dehn fillings on large hyperbolic 3-manifolds Toroidal Dehn fillings on large hyperbolic 3-manifolds

2005-08-15

arxiv.org/abs/math/0508250v1

Mathematics

Geometric Topology

28 pages, 29 figures

Scientific paper

We show that if a hyperbolic 3-manifold $M$ with a single torus boundary admits two Dehn fillings at distance 5, each of which contains an essential torus, then $M$ is a rational homology solid torus, which is not large in the sense of Wu. Moreover, one of the surgered manifold contains an essential torus which meets the core of the attached solid torus minimally in at most two points. This completes the determination of best possible upper bounds for the distance between two exceptional Dehn fillings yielding essential small surfaces in all ten cases for large hyperbolic 3-manifolds.

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