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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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          Author and article information

          Journal
          06 June 2014
          Article
          10.2140/agt.2014.14.3745
          1406.1597
          5555a9e9-a531-4409-8ed5-4254ba1ea544

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Algebr. Geom. Topol. 14 (2014) 3745-3763
          14 pages, 2 figures
          math.GT

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