Rank bounds in link Floer homology and detection results

  • Fraser Binns

    Boston College, Chestnut Hill, USA
  • Subhankar Dey

    The University of Alabama, Tuscaloosa, USA
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Abstract

Viewing the BRAID invariant as a generator of link Floer homology, we generalize work of Baldwin–Vela-Vick to obtain rank bounds on the next-to-top grading of knot Floer homology. These allow us to classify links with knot Floer homology of rank at most eight and prove a variant of a classification of links with Khovanov homology of low rank due to Xie–Zhang. In another direction, we use a variant of Ozsváth–Szabó's classification of collapsed filtered chain complexes to show that knot Floer homology detects and . Combining these techniques with the spectral sequences of Batson–Seed, Dowlin, and Lee, we can show that Khovanov homology likewise detects and .

Cite this article

Fraser Binns, Subhankar Dey, Rank bounds in link Floer homology and detection results. Quantum Topol. 16 (2025), no. 4, pp. 743–794

DOI 10.4171/QT/197