Floer homology and right-veering monodromy

TL;DR

This paper demonstrates that knot Floer complexes can determine if a fibered knot's monodromy is right-veering, providing a knot Floer-theoretic way to characterize tight contact structures and exploring applications to surgeries and foliations.

Contribution

It establishes a new method to detect right-veering monodromy using knot Floer homology, linking it to contact geometry and symplectic Floer homology.

Findings

Knot Floer complex detects right-veering monodromy

Characterizes tight contact structures via knot Floer homology

Applications to Dehn surgeries and taut foliations

Abstract

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of Honda, Kazez, and Matic. Our proof makes use of the relationship between the Heegaard Floer homology of mapping tori and the symplectic Floer homology of area-preserving surface diffeomorphisms. We describe applications of this work to Dehn surgeries and taut foliations.