2-knot homology and Roseman move

TL;DR

This paper extends Ng's combinatorial knot contact homology to construct an invariant for surface-knots in four-dimensional space using three-dimensional diagrams.

Contribution

It introduces a new invariant for surface-knots in ${f R}^4$ based on diagrammatic methods, expanding the scope of knot contact homology.

Findings

Constructed a surface-knot invariant in ${f R}^4$

Extended knot contact homology to higher dimensions

Provides a new tool for classifying surface-knots

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 diagrams in ${\mathbb{R}}^3$.