Volume 8, issue 1 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Knots in lens spaces with the $3$–sphere surgery

Toshio Saito

Algebraic & Geometric Topology 8 (2008) 53–79
Abstract

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 (p,q) is obtained by Berge’s surgery on a nontrivial nontorus doubly primitive knot in the 3–sphere, then |q| 5. To this end, we completely list up all such lens spaces with |q| < 5 and prove that they are obtained only by torus knots.

Keywords
Dehn surgery, lens space, doubly primitive knot, dual knot
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25
References
Publication
Received: 22 February 2006
Accepted: 7 November 2007
Published: 8 February 2008
Authors
Toshio Saito
Graduate School of Humanities and Sciences
Nara Women’s University
Kitauoya Nishi-machi
Nara 630–8506
Japan