Algebraic and Geometric Topology 3 (2003), paper no. 14, pages 435-472.

Small Seifert-fibered Dehn surgery on hyperbolic knots

John C. Dean

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

AMS subject classification. Primary: 57M25. Secondary: 57M27.

DOI: 10.2140/agt.2003.3.435

E-print: arXiv:math.GT/0306232

Submitted: 9 August 2002. (Revised: 7 February 2003.) Accepted: 4 April 2003. Published: 22 May 2003.

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

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