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2008 Knots in lens spaces with the $3$–sphere surgery
Toshio Saito
Algebr. Geom. Topol. 8(1): 53-79 (2008). DOI: 10.2140/agt.2008.8.53

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.

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Toshio Saito. "Knots in lens spaces with the $3$–sphere surgery." Algebr. Geom. Topol. 8 (1) 53 - 79, 2008. https://doi.org/10.2140/agt.2008.8.53

Information

Received: 22 February 2006; Accepted: 7 November 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1170.57008
MathSciNet: MR2377277
Digital Object Identifier: 10.2140/agt.2008.8.53

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2008 Mathematical Sciences Publishers

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