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Knot Floer homology, link Floer homology and link detection

Fraser Binns and Gage Martin

Algebraic & Geometric Topology 24 (2024) 159–181

We give new link detection results for knot and link Floer homology, inspired by recent work on Khovanov homology. We show that knot Floer homology detects T(2,4), T(2,6), T(3,3), L7n1 and the link T(2,2n) with the orientation of one component reversed. We show link Floer homology detects T(2,2n) and T(n,n), for all n. Additionally, we identify infinitely many pairs of links such that both links in the pair are each detected by link Floer homology but have the same Khovanov homology and knot Floer homology. Finally, we use some of our knot Floer detection results to give topological applications of annular Khovanov homology.

knot Floer homology, annular Khovanov homology, link detection
Mathematical Subject Classification
Primary: 57K10, 57K18
Received: 13 March 2021
Revised: 10 August 2022
Accepted: 26 August 2022
Published: 18 March 2024
Fraser Binns
Mathematics department
Boston College
Chestnut Hill, MA
United States
Gage Martin
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States

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