Berge–Gabai knots and L–space satellite operations

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2015-01-15

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Abstract

© 2014 Mathematical Sciences Publishers. All rights reserved. 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 [13] and Hom [17].

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10.2140/agt.2014.14.3745

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Hom, J, T Lidman and F Vafaee (2015). Berge–Gabai knots and L–space satellite operations. Algebraic & Geometric Topology, 14(6). pp. 3745–3763. 10.2140/agt.2014.14.3745 Retrieved from https://hdl.handle.net/10161/17371.

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