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(1,1) L-space knots

Greene, Joshua Evan and Lewallen, Sam and Vafaee, Faramarz (2018) (1,1) L-space knots. Compositio Mathematica, 154 (5). pp. 918-933. ISSN 0010-437X. doi:10.1112/S0010437X17007989.

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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.

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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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Alfred P. Sloan FoundationUNSPECIFIED
NSF Graduate Research FellowshipUNSPECIFIED
Issue or Number:5
Record Number:CaltechAUTHORS:20180516-100045096
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Official Citation:Greene, J., Lewallen, S., & Vafaee, F. (2018). (1,1) L-space knots. Compositio Mathematica, 154(5), 918-933. doi:10.1112/S0010437X17007989
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86419
Deposited By: Tony Diaz
Deposited On:18 May 2018 17:40
Last Modified:15 Nov 2021 20:38

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