Exceptional surgery on knots

Boyer, S.; Zhang, X.

doi:10.1090/S0273-0979-1994-00516-6

Exceptional surgery on knots
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Bull. Amer. Math. Soc. 31 (1994), 197-203 Request permission

Abstract:

Let M be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if M is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If M has a non-boundary-parallel, incompressible torus and is not a generalized 1-iterated torus knot complement, then there are at most three finite/cyclic fillings of maximal distance 1. Further, if M has a non-boundary-parallel, incompressible torus and is not a generalized 1- or 2-iterated torus knot complement and if M admits a cyclic filling of odd order, then M does not admit any other finite/cyclic filling. Relations between finite/cyclic fillings and other exceptional fillings are also discussed.

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