L-space surgery and twisting operation

Abstract

A knot in the 3-sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, i.e. a rational homology 3-sphere with the smallest possible Heegaard Floer homology. Given a knot K, take an unknotted circle c and twist K n times along c to obtain a twist family { K_n }. We give a sufficient condition for { K_n } to contain infinitely many L-space knots. As an application we show that for each torus knot and each hyperbolic Berge knot K, we can take c so that the twist family { K_n } contains infinitely many hyperbolic L-space knots. We also demonstrate that there is a twist family of hyperbolic L-space knots each member of which has tunnel number greater than one.

The final version, accepted for publication by Algebr. Geom. Topol

References in corpus (3)

• Knot Floer homology detects fibred knots
• On the knot Floer homology of twisted torus knots
• Berge-Gabai knots and L-space satellite operations

Cited by in corpus (3)

• Seifert vs slice genera of knots in twist families and a characterization of braid axes
• Asymmetric L-space knots
• L-space knots with tunnel number >1 by experiment