A cube of resolutions for knot Floer homology

TL;DR

This paper introduces a skein exact sequence for knot Floer homology involving singular knots, providing an explicit algebraic description based on braid projections, advancing computational and theoretical understanding.

Contribution

It develops a skein exact sequence for knot Floer homology involving singular knots and offers an explicit algebraic description using braid projections.

Findings

Established a skein exact sequence for knot Floer homology.

Provided an explicit algebraic description of knot Floer homology.

Connected knot Floer homology with braid projections.

Abstract

We develop a skein exact sequence for knot Floer homology, involving singular knots. This leads to an explicit, algebraic description of knot Floer homology in terms of a braid projection of the knot.