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      Berge-Gabai knots and L-space satellite operations

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          Abstract

          Let \(P(K)\) be a satellite knot where the pattern, \(P\), is a Berge-Gabai knot (i.e., a knot in the solid torus with a non-trivial solid torus Dehn surgery), and the companion, \(K\), is a non-trivial knot in \(S^3\). 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 and the first author.

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          Journal
          10.2140/agt.2014.14.3745
          1406.1597

          Geometry & Topology
          Geometry & Topology

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