# Transverse braids and combinatorial knot Floer homology

## TL;DR

This paper introduces a new combinatorial method to compute the transverse invariant in knot Floer homology, improving previous approaches by explicitly identifying the invariant for transverse links in braid diagrams.

## Contribution

The authors develop a novel combinatorial complex that computes knot Floer homology and explicitly identifies the transverse invariant within this framework.

## Key findings

- Successfully computes the transverse invariant for transverse links
- Provides a new combinatorial tool for knot Floer homology
- Enhances understanding of braid diagrams in knot theory

## Abstract

We describe a new method for combinatorially computing the transverse invariant in knot Floer homology. Previous work of the authors and Stone used braid diagrams to combinatorially compute knot Floer homology of braid closures. However, that approach was unable to explicitly identify the invariant of transverse links that naturally appears in braid diagrams. In this paper, we improve the previous approach in order to compute the transverse invariant. We define a new combinatorial complex that computes knot Floer homology and identify the BRAID invariant of transverse knots and links in the homology of this complex.