2-knot homology and Yoshikawa move

TL;DR

This paper extends Ng's combinatorial knot contact homology from classical knots to surface-knots in four-dimensional space using marked graph diagrams, providing a new invariant for higher-dimensional knot theory.

Contribution

The paper introduces a novel invariant for surface-knots in ${\mathbb{R}}^4$ based on marked graph diagrams, expanding the scope of contact homology.

Findings

Constructed a new invariant for surface-knots in ${\mathbb{R}}^4$

Extended Ng's knot contact homology to higher dimensions

Provides tools for distinguishing surface-knots using combinatorial methods

Abstract

Ng constructed an invariant of knots in ${\mathbb{R}}^3$, a combinatorial knot contact homology. Extending his study, we construct an invariant of surface-knots in ${\mathbb{R}}^4$ using marked graph diagrams.