Toroidal Dehn fillings on large hyperbolic 3-manifolds

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 manifolds 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.

Keywords

Dehn filling, toroidal Dehn filling, large manifold

2010 Mathematics Subject Classification

Primary 57N10. Secondary 57M50.

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Published 1 January 2006