Annular and boundary reducing Dehn fillings
Abstract
A manifold M is simple if it contains no essential disk, sphere, annulus or torus. If M is simple and two Dehn fillings M(r1), M(r2) are nonsimple, then there is an upper bound on (r1,r2), the geometric intersection number between r1 and r2. There are 10 possibilities, depending on the types of M(ri). In this paper it will be shown that if M(r1) contains an essential disk and M(r2) contains an essential annulus, then (r1,r2) is at most two. This completes the determination of the best possible upper bounds on (r1, r2) for all ten cases.
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