Communications in Analysis and Geometry
Volume 14 (2006)
Toroidal Dehn fillings on large hyperbolic 3-manifolds
Pages: 565 – 601
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.
Dehn filling; toroidal Dehn filling; large manifold
2010 Mathematics Subject Classification
Primary 57N10. Secondary 57M50.