Dehn surgery on knots in solid tori creating essential annuli
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- by Chuichiro Hayashi and Kimihiko Motegi PDF
- Trans. Amer. Math. Soc. 349 (1997), 4897-4930 Request permission
Abstract:
Let $M$ be a $3$-manifold obtained by performing a Dehn surgery on a knot in a solid torus. In the present paper we study when $M$ contains a separating essential annulus. It is shown that $M$ does not contain such an annulus in the majority of cases. As a corollary, we prove that symmetric knots in the $3$-sphere which are not periodic knots of period $2$ satisfy the cabling conjecture. This is an improvement of a result of Luft and Zhang. We have one more application to a problem on Dehn surgeries on knots producing a Seifert fibred manifold over the $2$-sphere with exactly three exceptional fibres.References
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Additional Information
- Chuichiro Hayashi
- Affiliation: Department of Mathematics, Faculty of Science, Gakushuin University, Mejiro 1-5-1, Toshima-ku, Tokyo 171, Japan
- Email: chuichiro.hayashi@gakushuin.ac.jp
- Kimihiko Motegi
- Affiliation: Department of Mathematics, College of Humanities & Sciences, Nihon University Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156, Japan
- MR Author ID: 254668
- Email: motegi@math.chs.nihon-u.ac.jp
- Received by editor(s): June 28, 1995
- Received by editor(s) in revised form: January 30, 1996
- Additional Notes: The first author was supported in part by Fellowships of the Japan Society for the Promotion of Science for Japanese Junior Scientists, and the second author was supported in part by Grant-in-Aid for Encouragement of Young Scientists 07740077, The Ministry of Education, Science and Culture.
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 4897-4930
- MSC (1991): Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9947-97-01723-6
- MathSciNet review: 1373637