Knot Floer homology of satellite knots with \((1, 1)\) patterns (Q6132655)

The author gives ``an immersed-curve approach to compute the knot Floer chain complexes of the corresponding satellite knots. In particular, this approach provides a convenient way to compute the knot concordance invariant $\tau$.'' This paper extends Hanselman-Rasmussen-Watson's work [\textit{J. Hanselman} et al., J. Am. Math. Soc. 37, No. 2, 391--498 (2024; Zbl 07798119)] to the context of knot Floer homology of satellite knots. It translates the pairing of the filtered type A structure $CFA(S^1\times D^2, P)$ and the (unfiltered) type D structure $CFD(X_K)$ to the Lagrangian Floer homology on the torus, and hence obtain the knot Floer homology of the satellite knot $P(K)$.