Volume 14, issue 6 (2014)

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Berge–Gabai knots and L–space satellite operations

Jennifer Hom, Tye Lidman and Faramarz Vafaee

Algebraic & Geometric Topology 14 (2014) 3745–3763
Abstract

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].

Keywords
L–space, Berge–Gabai knot, satellite knot, Dehn surgery
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58
References
Publication
Received: 26 June 2014
Accepted: 8 August 2014
Published: 15 January 2015
Authors
Jennifer Hom
Department of Mathematics
Columbia University
New York, NY 10027
USA
Tye Lidman
Department of Mathematics
University of Texas at Austin
Austin, TX 78712
USA
Faramarz Vafaee
Mathematics Department
California Institute of Technology
Pasadena, CA 91125
USA