A mnemonic for the Lipshitz–Ozsváth–Thurstoncorrespondence

Kotelskiy, Artem; Watson, Liam; Zibrowius, Claudius

Abstract

When k is a field, type D structures over the algebra k[u,v]∕(uv) are equivalent to immersed curves decorated with local systems in the twice-punctured disk. Consequently, knot Floer homology, as a type D structure over k[u,v]∕(uv), can be viewed as a set of immersed curves. With this observation as a starting point, given a knot K in S3, we realize the immersed curve invariant HF (S3\∘ν(K)) of Hanselman, Rasmussen and Watson by converting the twice-punctured disk to a once-punctured torus via a handle attachment. This recovers a result of Lipshitz, Ozsváth and Thurston calculating the bordered invariant of S3\∘ν(K)) in terms of the knot Floer homology of K.

Citation

Kotelskiy, A., Watson, L., & Zibrowius, C. (2023). A mnemonic for the Lipshitz–Ozsváth–Thurstoncorrespondence. Algebraic & geometric topology, 23(6), 2519-2543. https://doi.org/10.2140/agt.2023.23.2519

• Journal Article Type: Article
• Acceptance Date: Feb 11, 2022
• Online Publication Date: Sep 7, 2023
• Publication Date: Sep 7, 2023
• Deposit Date: Feb 19, 2024
• Publicly Available Date: Feb 19, 2024
• Journal: Algebraic & Geometric Topology
• Print ISSN: 1472-2747
• Electronic ISSN: 1472-2739
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 6
• Pages: 2519-2543
• DOI: https://doi.org/10.2140/agt.2023.23.2519
• Keywords: Geometry and Topology
• Public URL: https://durham-repository.worktribe.com/output/2269521