Immersed surfaces and Seifert fibered surgery on Montesinos knots

Abstract

We will use immersed surfaces to study Seifert fibered surgery on Montesinos knots, and show that if $\frac{1}{q_1-1}+\frac{1}{q_2-1}+\frac{1}{q_3-1}\le 1$ 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.

Cited by in corpus (2)

• Small Seifert fibered surgery on hyperbolic pretzel knots
• Exceptional surgeries on $(-2,p,p)$-pretzel knots