Geodesic
Knots in lens spaces with the 3–sphere surgery
Saito, Toshio1
1Graduate School of Humanities and Sciences, Nara Women’s University, Kitauoya Nishi-machi, Nara 630–8506, Japan
Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 53-79
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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 (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.

DOI : 10.2140/agt.2008.8.53
Keywords: Dehn surgery, lens space, doubly primitive knot, dual knot

Saito, Toshio  1

1 Graduate School of Humanities and Sciences, Nara Women’s University, Kitauoya Nishi-machi, Nara 630–8506, Japan 
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Saito, Toshio. Knots in lens spaces with the 3–sphere surgery. Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 53-79. doi: 10.2140/agt.2008.8.53

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