Toroidal Seifert fibered surgeries on alternating knots

Abstract

We give a complete classification of toroidal Seifert fibered surgeries on alternating knots. Precisely, we show that if an alternating knot admits a toroidal Seifert fibered surgery, then the knot is either the trefoil knot and the surgery slope is zero, or the connected sum of a (2,p)-torus knot and a (2,q)-torus knot and the surgery slope is 2(p+q) with |p|, |q| at least three.

4 pages

References in corpus (2)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Exceptional surgeries on alternating knots

Cited by in corpus (1)

• Exceptional surgeries on alternating knots