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Abstract
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In this paper, we improve a necessary condition which we gave in [Topology Appl.
154 (2007) 1502–1515], for 1–bridge braids in lens spaces to admit an integral surgery
yielding the 3–sphere. As an application, we prove that if the lens space of type
is obtained
by Berge’s surgery on a nontrivial nontorus doubly primitive knot in the 3–sphere,
then .
To this end, we completely list up all such lens spaces with
and
prove that they are obtained only by torus knots.
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Keywords
Dehn surgery, lens space, doubly primitive knot, dual knot
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25
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Publication
Received: 22 February 2006
Accepted: 7 November 2007
Published: 8 February 2008
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