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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Exceptional surgery on knots


Authors: S. Boyer and X. Zhang
Journal: Bull. Amer. Math. Soc. 31 (1994), 197-203
MSC: Primary 57N10; Secondary 57M25
MathSciNet review: 1260518
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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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DOI: http://dx.doi.org/10.1090/S0273-0979-1994-00516-6
PII: S 0273-0979(1994)00516-6
Article copyright: © Copyright 1994 American Mathematical Society