## Algebraic & Geometric Topology

### 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 $S3$. 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

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

Dates
Revised: 7 February 2003
Accepted: 4 April 2003
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882379

Digital Object Identifier
doi:10.2140/agt.2003.3.435

Mathematical Reviews number (MathSciNet)
MR1997325

Zentralblatt MATH identifier
1021.57002

#### Citation

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. https://projecteuclid.org/euclid.agt/1513882379

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