Symmetry of knots and cyclic surgery
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- by Shi Cheng Wang and Qing Zhou PDF
- Trans. Amer. Math. Soc. 330 (1992), 665-676 Request permission
Abstract:
If a nontorus knot $K$ admits a symmetry which is not a strong inversion, then there exists no nontrivial cyclic surgery on $K$. No surgery on a symmetric knot can produce a fake lens space or a $3$-manifold $M$ with $|{\pi _1}(M)|= 2$. 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 $3$-manifold $M$ with $|{\pi _1}(M)| < 5$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 330 (1992), 665-676
- MSC: Primary 57M25; Secondary 57N12
- DOI: https://doi.org/10.1090/S0002-9947-1992-1031244-6
- MathSciNet review: 1031244