Asymmetric L-space knots

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 $S^1\times S^2$.

References in corpus (2)

• Floer Simple Manifolds and L-Space Intervals
• Bounds on alternating surgery slopes

Cited by in corpus (2)

• L-space knots with tunnel number >1 by experiment
• Chainmail links and L-spaces