Floer homology and right-veering monodromy

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.

arXiv comment30 pages, 4 figures; v2: accepted version

References in corpus (10)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Khovanov homology detects the trefoils
• The reduced knot Floer complex
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• On knot Floer homology and cabling
• Fractional Dehn twists in knot theory and contact topology
• A note on the knot Floer homology of fibered knots
• Khovanov homology detects the figure-eight knot
• Persistently foliar composite knots