Cyclic surgery on knots

Wang, Shi Cheng

doi:10.1090/S0002-9939-1989-0984820-6

Cyclic surgery on knots
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Proc. Amer. Math. Soc. 107 (1989), 1091-1094 Request permission

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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