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Published May 2018 | Submitted
Journal Article Open

(1,1) L-space knots


We characterize the (1,1) knots in the 3-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non-trivial L-space surgeries. We also recover a characterization of the Berge manifold among 1-bridge braid exteriors.

Additional Information

© The Authors 2018. Published online: 20 March 2018. We thank Matt Hedden, Jen Hom, David Krcatovich, Adam Levine, Clayton McDonald, Yi Ni, and Alex Zupan for helpful conversations. We thank the referee for a very thorough and thoughtful review. Sam Lewallen would like to thank Zoltán Szabó for suggesting he study (1; 1) L-space knots, and both Zoltán and Liam Watson for their interest and encouragement. JEG was supported by NSF CAREER Award DMS-1455132 and an Alfred P. Sloan Foundation Research Fellowship. SL was supported by an NSF Graduate Research Fellowship.

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