Holomorphic polygons and the bordered Heegaard Floer homology of link complements

Hockenhull, Thomas

doi:10.2140/agt.2025.25.3145

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Holomorphic polygons and the bordered Heegaard Floer homology of link complements

Thomas Hockenhull

Algebraic & Geometric Topology 25 (2025) 3145–3224

DOI: 10.2140/agt.2025.25.3145

Abstract

We describe the construction of an $𝒜_{\infty}$ multimodule in terms of counts of holomorphic polygons in a series of Heegaard multidiagrams. We show that this is quasi-isomorphic to the type-A bordered-sutured invariant of a link complement with a view to calculating, in the sequel, these invariants in terms of the link Floer homology of the corresponding link.

Keywords

Heegaard Floer homology, bordered Floer homology, knot theory, low-dimensional topology, symplectic geometry, knot theory

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 3 April 2019

Revised: 18 July 2023

Accepted: 5 June 2024

Published: 1 October 2025

Authors

Thomas Hockenhull
Frome Somerset United Kingdom

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Volume 25, issue 6 (2025)