Knot Floer homology and fixed points

If $K$ is a fibered knot in a closed, oriented $3$–manifold $Y$ with fiber $F$, and $\widehat{HFK}(Y,K,[F],g(F)-1;\mathbb{Z}\mathrm{/}2\mathbb{Z})$ has rank $r$, then the monodromy of $K$ is freely isotopic to a diffeomorphism with at most $r-1$ fixed points. This generalizes earlier work of Baldwin–Hu–Sivek and Ni. We also clarify a misleading formula in Cotton-Clay’s computation of the symplectic Floer homology of mapping classes of surfaces.