Cable knots are not thin

Abstract

Using the Bordered Floer theory of Lipshitz-Ozsváth-Thurston we prove that the $(p,q)$-cables of any non-trivial knots are not Heegaard Floer homologically thin. Using the proof and a theorem of Zemke, we find a larger set of satellite knots which is a proper superset of the set of all cable knots, having the same property.

Revised version, accepted to be published in Algebraic and Geometric Topology

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Cited by in corpus (1)

• Twisted Mazur pattern satellite knots and bordered Floer theory