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2016 L-space surgery and twisting operation
Kimihiko Motegi
Algebr. Geom. Topol. 16(3): 1727-1772 (2016). DOI: 10.2140/agt.2016.16.1727


A knot in the 3–sphere is called an L-space knot if it admits a nontrivial Dehn surgery yielding an L-space, ie 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 {Kn}. We give a sufficient condition for {Kn} 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 {Kn} 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.


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Kimihiko Motegi. "L-space surgery and twisting operation." Algebr. Geom. Topol. 16 (3) 1727 - 1772, 2016.


Received: 28 April 2015; Revised: 16 August 2015; Accepted: 10 September 2015; Published: 2016
First available in Project Euclid: 28 November 2017

zbMATH: 1345.57015
MathSciNet: MR3523053
Digital Object Identifier: 10.2140/agt.2016.16.1727

Primary: 57M25, 57M27
Secondary: 57N10

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.16 • No. 3 • 2016
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