Small Seifert-fibered Dehn surgery on hyperbolic knots

Abstract

In this paper, we define the primitive/Seifert-fibered property for a knot in $S^3$. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base $S^2$ and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of examples of primitive/Seifert-fibered knots. By analyzing the twisted torus knots, we prove that nearly all possible triples of multiplicities of the critical fibers arise via Dehn surgery on primitive/Seifert-fibered knots.