Cabling in terms of immersed curves

Hanselman, Jonathan; Watson, Liam

doi:10.2140/gt.2023.27.925

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Cabling in terms of immersed curves

Jonathan Hanselman and Liam Watson

Geometry & Topology 27 (2023) 925–952

DOI: 10.2140/gt.2023.27.925

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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Volume 27, issue 3 (2023)