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Asymmetric L–space knots

Kenneth L Baker and John Luecke

Geometry & Topology 24 (2020) 2287–2359
Abstract

We construct the first examples of asymmetric L–space knots in S3. More specifically, we exhibit a construction of hyperbolic knots in S3 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 S3 which are not strongly invertible. The construction also immediately extends to produce asymmetric L–space knots in any lens space, including S1 × S2.

Keywords
L–space, L–space knot, asymmetric knot, alternating knot, alternating link, alternating surgery, branched double cover, Dehn surgery, lashings
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57M12, 57R58
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
Authors
Kenneth L Baker
Department of Mathematics
University of Miami
Coral Gables, FL
United States
John Luecke
Department of Mathematics
The University of Texas at Austin
Austin, TX
United States