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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Dehn surgery on knots in solid tori
creating essential annuli

Authors: Chuichiro Hayashi and Kimihiko Motegi
Journal: Trans. Amer. Math. Soc. 349 (1997), 4897-4930
MSC (1991): Primary 57M25
MathSciNet review: 1373637
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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.

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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

Kimihiko Motegi
Affiliation: Department of Mathematics, College of Humanities & Sciences, Nihon University Sakurajosui 3-25-40, Setagaya-ku, Tokyo 156, Japan

Keywords: Dehn surgery, essential annulus, cabling conjecture, Seifert fibred manifold, Scharlemann cycle
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.
Article copyright: © Copyright 1997 American Mathematical Society