Berge–Gabai knots and L–space satellite operations

Hom, Jennifer¹ ; Lidman, Tye² ; Vafaee, Faramarz³

¹Department of Mathematics, Columbia University, New York, NY 10027, USA
²Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA
³Mathematics Department, California Institute of Technology, Pasadena, CA 91125, USA

Algebraic and Geometric Topology, Tome 14 (2014) no. 6, pp. 3745-3763

Résumé

Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [Int. Math. Res. Not. 2009 (2009) 2248–2274] and Hom [Algebr. Geom. Topol. 11 (2011) 219–223].

Détail

DOI : 10.2140/agt.2014.14.3745

Classification : 57M25, 57M27, 57R58
Keywords: L–space, Berge–Gabai knot, satellite knot, Dehn surgery

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