Small Seifert-fibered Dehn surgery on hyperbolic knots

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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

References

Forward citations

Publication

Received: 9 August 2002

Revised: 7 February 2003

Accepted: 4 April 2003

Published: 22 May 2003

Authors

John C Dean
818 Forest Ave. Oak Park, IL 60302 USA

Volume 3, issue 1 (2003)

John C Dean