Joint Los Angeles Topology Seminar

A satellite operator on knots is called an L-space satellite operator if the 2-component link, consisting of the pattern and the meridian of the solid torus, is an L-space link. Examples of such operators include cabling, Whitehead double and Mazur patterns. We present an algorithm to compute the knot Floer homology of the resulting knot in terms of the knot Floer homology of the companion knot, as well as the Alexander polynomials of the 2-component link and the pattern. This algorithm is based on the link surgery formula of Manolescu and Ozsváth, together with a reinterpretation and a connected sum formula of it by Zemke. A key ingredient in this algorithm is a formality result for 2-component L-space links, which says we can determine the knot Floer chain complex of such a link from the Alexander polynomial of it and its sublinks. This is joint work with Ian Zemke and Hugo Zhou.