Dehn surgery on knots in solid tori creating essential annuli

Hayashi, Chuichiro; Motegi, Kimihiko

doi:10.1090/S0002-9947-97-01723-6

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.

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