Symmetry of knots and cyclic surgery

Authors:
Shi Cheng Wang and Qing Zhou

Journal:
Trans. Amer. Math. Soc. **330** (1992), 665-676

MSC:
Primary 57M25; Secondary 57N12

MathSciNet review:
1031244

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Abstract: If a nontorus knot admits a symmetry which is not a strong inversion, then there exists no nontrivial cyclic surgery on . No surgery on a symmetric knot can produce a fake lens space or a -manifold with . This generalizes the result of Culler-Gordon-Luecke-Shalen-Bleiler-Scharlemann and supports the conjecture that no nontrivial surgery on a nontrivial knot yields a -manifold with .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1031244-6

Article copyright:
© Copyright 1992
American Mathematical Society