Small Seifert-fibered Dehn surgery on hyperbolic knots

Dean, John C¹

¹818 Forest Ave., Oak Park, IL 60302, USA

Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 435-472

Résumé

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.

Détail

DOI : 10.2140/agt.2003.3.435

Keywords: Dehn surgery, hyperbolic knot, Seifert-fibered space, exceptional surgery

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