Immersed surfaces and Seifert fibered surgery on Montesinos knots

Wu, Ying-Qing

doi:10.1090/S0002-9947-2012-05708-4

Immersed surfaces and Seifert fibered surgery on Montesinos knots
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Trans. Amer. Math. Soc. 365 (2013), 2469-2488 Request permission

Abstract:

We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if $\frac 1{q_1-1} + \frac 1{q_2-1} + \frac 1{q_3-1} \leq 1$, then a Montesinos knot $K(\frac {p_1}{q_1}, \frac {p_2}{q_2}, \frac {p_3}{q_3})$ admits no atoroidal Seifert fibered surgery.

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