Some knots in S^1 x S^2 with lens space surgeries

@article{Baker2013SomeKI,
  title={Some knots in S^1 x S^2 with lens space surgeries},
  author={Kenneth L. Baker and Dorothy Buck and Ana G. Lecuona},
  journal={arXiv: Geometric Topology},
  year={2013}
}
We propose a classification of knots in S^1 x S^2 that admit a longitudinal surgery to a lens space. Any lens space obtainable by longitudinal surgery on some knots in S^1 x S^2 may be obtained from a Berge-Gabai knot in a Heegaard solid torus of S^1 x S^2, as observed by Rasmussen. We show that there are yet two other families of knots: those that lie on the fiber of a genus one fibered knot and the `sporadic' knots. All these knots in S^1 x S^2 are both doubly primitive and spherical braids… 

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