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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 S3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S2 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
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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