# 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}
}
• Published 27 February 2013
• Mathematics
• arXiv: Geometric Topology
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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