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2003 Small Seifert-fibered Dehn surgery on hyperbolic knots
John C Dean
Algebr. Geom. Topol. 3(1): 435-472 (2003). DOI: 10.2140/agt.2003.3.435

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.

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John C Dean. "Small Seifert-fibered Dehn surgery on hyperbolic knots." Algebr. Geom. Topol. 3 (1) 435 - 472, 2003. https://doi.org/10.2140/agt.2003.3.435

Information

Received: 9 August 2002; Revised: 7 February 2003; Accepted: 4 April 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1021.57002
MathSciNet: MR1997325
Digital Object Identifier: 10.2140/agt.2003.3.435

Subjects:
Primary: 57M25
Secondary: 57M27

Rights: Copyright © 2003 Mathematical Sciences Publishers

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Vol.3 • No. 1 • 2003
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