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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Cyclic surgery on knots


Author: Shi Cheng Wang
Journal: Proc. Amer. Math. Soc. 107 (1989), 1091-1094
MSC: Primary 57N10; Secondary 57M25
MathSciNet review: 984820
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Abstract: We get a necessary condition under which a nonsimple knot (i.e. a satellite knot) admits a nontrivial surgery producing a lens space. Interesting corollaries are: (1) if a lens space can be obtained from a nontrivial surgery on a nonsimple knot, then the order of its fundamental group is not smaller than 23; (2) any nonsimple knot admits at most one nontrivial surgery which produces a lens space.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0984820-6
PII: S 0002-9939(1989)0984820-6
Article copyright: © Copyright 1989 American Mathematical Society