#### Volume 3, issue 1 (2003)

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Small Seifert-fibered Dehn surgery on hyperbolic knots

### John C Dean

Algebraic & Geometric Topology 3 (2003) 435–472
 arXiv: math.GT/0306232
##### 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.

##### Keywords
Dehn surgery, hyperbolic knot, Seifert-fibered space, exceptional surgery
Primary: 57M25
Secondary: 57M27