In joint work with J Rasmussen (Proc. Lond. Math. Soc. (3) 125 (2022) 879–967), we gave an interpretation of Heegaard Floer homology for manifolds with torus boundary in terms of immersed curves in a punctured torus. In particular, knot Floer homology is captured by this invariant (arXiv 1810.10355). Appealing to earlier work of the authors on bordered Floer homology (Geom. Topol. 27 (2023) 823–924), we give a formula for the behaviour of these immersed curves under cabling.
All Science Journal Classification (ASJC) codes
- Geometry and Topology