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Asymmetric L–space
knots
Kenneth L Baker and John Luecke |
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Geometry & Topology 24 (2020) 2287–2359
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Abstract |
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We construct the first examples of asymmetric L–space knots in . More specifically, we exhibit a construction of hyperbolic knots in with both (i) a surgery that may be realized as a surgery on a strongly invertible link such that the result of the surgery is the double branched cover of an alternating link and (ii) trivial isometry group. In particular, this produces L–space knots in which are not strongly invertible. The construction also immediately extends to produce asymmetric L–space knots in any lens space, including . |
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Keywords
L–space, L–space knot, asymmetric knot, alternating knot,
alternating link, alternating surgery, branched double
cover, Dehn surgery, lashings
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57M12, 57R58
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References |
Publication
Received: 29 November 2017
Revised: 18 April 2019
Accepted: 26 May 2019
Published: 29 December 2020
Proposed: Ciprian Manolescu
Seconded: András I Stipsicz, Peter Ozsváth
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Authors |
| Kenneth L Baker | |
| Department of Mathematics University of Miami Coral Gables, FL United States |
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| John Luecke | |
| Department of Mathematics The University of Texas at Austin Austin, TX United States |
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