Applying Lipson's state models to marked graph diagrams of surface-links

TL;DR

This paper explores how Lipson's state models, originally used for classical link invariants, can be applied to marked graph diagrams of surface-links to potentially induce new surface-link invariants.

Contribution

It extends Lipson's state models to the context of surface-links, analyzing conditions under which they produce valid invariants.

Findings

Lipson's state models can be adapted to marked graph diagrams of surface-links.

Conditions identified for Lipson's models to induce surface-link invariants.

Potential for new invariants in surface-link theory using Lipson's models.

Abstract

A. S. Lipson constructed two state models yielding the same classical link invariant obtained from the Kauffman polynomial $F(a,z)$. In this paper, we apply Lipson's state models to marked graph diagrams of surface-links, and observe when they induce surface-link invariants.