Fractional Dehn twist coefficients and rank bounds for categorified link invariants

Abstract

We give two new lower bounds on the rank of categorified link invariants: one on the link Floer homology of fibered links in terms of the fractional Dehn twist coefficients of their monodromies, and another, as a corollary, on the annular Khovanov homology of braid closures in terms of the fractional Dehn twist coefficient of the braid. The most important technical component of the proof is that we determine the behaviour of the link Floer homology of fibered links under adding boundary Dehn twists to their monodromies in the next to top Alexander grading.