A note on knot Floer homology of satellite knots with (1,1)-patterns

Shen, Weizhe

doi:10.2140/agt.2025.25.3271

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ISSN (electronic): 1472-2739

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A note on knot Floer homology of satellite knots with $(1,1)$-patterns

Weizhe Shen

Algebraic & Geometric Topology 25 (2025) 3271–3286

DOI: 10.2140/agt.2025.25.3271

Abstract

We prove that if $P$ is a $(1, 1)$ -pattern, then the two inequalities $\dim \hat{HFK} (P (K)) \geq \dim \hat{HFK} (P (U))$ and $\dim \hat{HFK} (P (K)) \geq \dim \hat{HFK} (K)$ hold for the unknot $U \subset S^{3}$ and any companion $K \subset S^{3}$ .

Keywords

(1,1)-pattern, satellite knot, knot Floer homology

Mathematical Subject Classification

Primary: 57K18

References

Publication

Received: 22 September 2022

Revised: 29 October 2023

Accepted: 3 January 2024

Published: 1 October 2025

Authors

Weizhe Shen
School of Mathematics Georgia Institute of Technology Atlanta, GA United States

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Volume 25, issue 6 (2025)