Small Seifert-fibered Dehn surgery on hyperbolic knots

By John C. Dean. 2003

76 citations recorded by the source corpus.

In this paper, we dene the primitive/Seifert-bered property for a knot in S 3 . If satised, the property ensures that the knot has a Dehn surgery that yields a small Seifert-bered space (i.e. base S 2 and three or fewer critical bers). Next we describe the twisted torus knots, which provide an abundance of examples of primitive/Seifert-bered knots. By analyzing the twisted torus knots, we prove that nearly all possible triples of multiplicities of the critical bers arise via Dehn surgery on primitive/Seifert-bered knots.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b667eb09cbccfd6f068ca467461e5fa7301dcfec

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In Geometry and Topology

1. Bruno Martelli
2. Carlo Petronio
3. Cameron McA. Gordon
4. J. Luecke
5. Feng Luo

Citations in the corpus

• Dehn Filling of the "Magic" 3-manifold (2002, background): “Other knots in S3 with Seifert surgeries are also described in [7, 8, 22].”
• Non-integral Toroidal Dehn Surgeries (2004, background): “true of the Berge knots [1], which are the only known hyperbolic knots with lens space surgeries, and the knots of Dean [ 5 ], which have small Seifert fiber space surgeries.”