Algebraic & Geometric Topology 8 (2008) 53–79

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.

Keywords

Dehn surgery, lens space, doubly primitive knot, dual knot

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 22 February 2006
Accepted: 7 November 2007
Published: 8 February 2008

Authors