Symmetry of knots and cyclic surgery

Shicheng Wang; Qing Zhou

doi:10.1090/S0002-9947-1992-1031244-6

Symmetry of knots and cyclic surgery

Shicheng Wang
, Qing Zhou

数学科学学院

Peking University
Ruhr University Bochum
University of California at Los Angeles

科研成果: 期刊稿件 › 文章 › 同行评审

18 引用（Scopus）

摘要

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 |π₁(M)|=2.This generalizes the result of Culler-Gordon-Luecke-Shalen- Bleiler-Scharlemann and supports the conjecture thatno nontrivial surgery on a nontrivial knot yields a 3-manifoldM with |π₁(M)|+5.

源语言	英语
页（从-至）	665-676
页数	12
期刊	Transactions of the American Mathematical Society
卷	330
期	2
DOI	https://doi.org/10.1090/S0002-9947-1992-1031244-6
出版状态	已出版 - 4月 1992

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10.1090/S0002-9947-1992-1031244-6

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引用此

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AB - 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 |π1(M)|=2.This generalizes the result of Culler-Gordon-Luecke-Shalen- Bleiler-Scharlemann and supports the conjecture thatno nontrivial surgery on a nontrivial knot yields a 3-manifoldM with |π1(M)|+5.

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Symmetry of knots and cyclic surgery

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