Abstract
A knot in the –sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, ie a rational homology –sphere with the smallest possible Heegaard Floer homology. Given a knot , take an unknotted circle and twist times along to obtain a twist family . We give a sufficient condition for to contain infinitely many L-space knots. As an application we show that for each torus knot and each hyperbolic Berge knot , we can take so that the twist family 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.
Citation
Kimihiko Motegi. "L-space surgery and twisting operation." Algebr. Geom. Topol. 16 (3) 1727 - 1772, 2016. https://doi.org/10.2140/agt.2016.16.1727
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