# 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…

## 18 Citations

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### The Poincaré homology sphere, lens space surgeries, and some knots with tunnel number two

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### Tunnel number one knots satisfy the Berge Conjecture.

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### LENS SPACE SURGERIES ALONG CERTAIN 2-COMPONENT LINKS RELATED WITH PARK’S RATIONAL BLOW DOWN, AND REIDEMEISTER-TURAEV TORSION

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Abstract We study lens space surgeries along two different families of 2-component links, denoted by ${A}_{m, n} $ and ${B}_{p, q} $, related with the rational homology $4$-ball used in J. Park’s…

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In this paper we use an approach based on dynamics to prove that if $K\subset S^3$ is a tunnel number one knot which admits a Dehn filling resulting in a lens space $L$ then $K$ is either a Berge…

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Abstract We study lens space surgeries along two different families of 2-component links, denoted by ${A}_{m, n} $ and ${B}_{p, q} $, related with the rational homology $4$-ball used in J. Park’s…

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