Fibered links whose monodromy twists many times around a boundary component have large next-to-top link Floer homology, and braid closures with large fractional Dehn twist coefficient have large annular Khovanov homology.
Cabling in terms of immersed curves
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abstract
In joint work with J. Rasmussen, we gave an interpretation of Heegaard Floer homology for manifolds with torus boundary in terms of immersed curves in a punctured torus. In particular, knot Floer homology is captured by this invariant. Appealing to earlier work of the authors on bordered Floer homology, we give a formula for the behaviour of these immersed curves under cabling.
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Fractional Dehn twist coefficients and rank bounds for categorified link invariants
Fibered links whose monodromy twists many times around a boundary component have large next-to-top link Floer homology, and braid closures with large fractional Dehn twist coefficient have large annular Khovanov homology.