Algebraic & Geometric Topology

Small Seifert-fibered Dehn surgery on hyperbolic knots

John C Dean

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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.

Article information

Algebr. Geom. Topol., Volume 3, Number 1 (2003), 435-472.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Dehn surgery hyperbolic knot Seifert-fibered space exceptional surgery


Dean, John C. Small Seifert-fibered Dehn surgery on hyperbolic knots. Algebr. Geom. Topol. 3 (2003), no. 1, 435--472. doi:10.2140/agt.2003.3.435.

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