Knot Floer homology of fibred knots and Floer homology of surface diffeomorphisms

TL;DR

This paper establishes a deep connection between the Knot Floer homology of fibred knots and the fixed point Floer homology of surface diffeomorphisms, revealing new insights into their algebraic and geometric structures.

Contribution

It proves an isomorphism between the Knot Floer homology of fibred knots and fixed point Floer homology of monodromy maps, linking knot theory and surface dynamics.

Findings

Knot Floer homology of fibred knots relates to fixed point Floer homology.

Isomorphism established at Alexander grading 1-g.

Provides new tools for studying fibred knots via surface diffeomorphisms.

Abstract

We prove that the Knot Floer homology group of a fibred knot of genus g in the Alexander grading 1-g is isomorphic to a version of the fixed point Floer homology of an area-preserving representative of the monodromy.