#### Volume 24, issue 5 (2020)

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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 ${S}^{3}$. More specifically, we exhibit a construction of hyperbolic knots in ${S}^{3}$ 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 ${S}^{3}$ which are not strongly invertible. The construction also immediately extends to produce asymmetric L–space knots in any lens space, including ${S}^{1}×{S}^{2}$.

##### 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