Asymmetric L–space knots

Baker, Kenneth L¹ ; Luecke, John²

¹ Department of Mathematics, University of Miami, Coral Gables, FL, United States
² Department of Mathematics, The University of Texas at Austin, Austin, TX, United States

Geometry & topology, Tome 24 (2020) no. 5, pp. 2287-2359.

Résumé

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 $S^1\times S^2$.

Détail

DOI : 10.2140/gt.2020.24.2287

Classification : 57M25, 57M27, 57M12, 57R58
Keywords: L–space, L–space knot, asymmetric knot, alternating knot, alternating link, alternating surgery, branched double cover, Dehn surgery, lashings

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