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Cabling in terms of immersed curves

Jonathan Hanselman and Liam Watson

Geometry & Topology 27 (2023) 925–952
Abstract

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.

Keywords
knot Floer homology, bordered Heegaard Floer homology, immersed curves, cabling, concordance
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 12 August 2019
Revised: 22 November 2019
Accepted: 21 August 2021
Published: 8 June 2023
Proposed: Ciprian Manolescu
Seconded: Peter Ozsváth, András I Stipsicz
Authors
Jonathan Hanselman
Department of Mathematics
Princeton University
Princeton, NJ
United States
Liam Watson
Department of Mathematics
University of British Columbia
Vancouver BC
Canada

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