Presentation of immersed surface-links by marked graph diagrams

TL;DR

This paper extends the diagrammatic method for representing surface-links in 4-space to include immersed surface-links, introducing moves on diagrams that preserve their isotopy classes.

Contribution

It introduces a new presentation method for immersed surface-links using marked graph diagrams and defines moves that preserve their isotopy classes.

Findings

Extended marked graph diagram method to immersed surface-links

Defined moves on diagrams that preserve isotopy classes

Provided a framework for classifying immersed surface-links

Abstract

It is well known that surface-links in 4-space can be presented by diagrams on the plane of 4-valent spatial graphs with makers on the vertices, called marked graph diagrams. In this paper we extend the method of presenting surface-links by marked graph diagrams to presenting immersed surface-links. We also give some moves on marked graph diagrams that preserve the ambient isotopy classes of their presenting immersed surface-links.