Algebraic and Geometric Topology 3 (2003),
paper no. 14, pages 435-472.
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 S^3. If satisfied, the property ensures that the knot has a
Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2
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.
Keywords.
Dehn surgery, hyperbolic knot, Seifert-fibered space, exceptional surgery
AMS subject classification.
Primary: 57M25.
Secondary: 57M27.
DOI: 10.2140/agt.2003.3.435
E-print: arXiv:math.GT/0306232
Submitted: 9 August 2002.
(Revised: 7 February 2003.)
Accepted: 4 April 2003.
Published: 22 May 2003.
Notes on file formats
John C. Dean
818 Forest Ave., Oak Park, IL 60302, USA
Email: dean_john@yahoo.com
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