Presentation of immersed surface-links by marked graph diagrams

Abstract

It is well known that surface-links in [Formula: see text]-space can be presented by diagrams on the plane of [Formula: see text]-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.