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Abstract
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In this paper, we define the primitive/Seifert-fibered property for a knot in
. If satisfied,
the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space
(i.e. base
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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Keywords
Dehn surgery, hyperbolic knot, Seifert-fibered space,
exceptional surgery
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Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
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Publication
Received: 9 August 2002
Revised: 7 February 2003
Accepted: 4 April 2003
Published: 22 May 2003
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