Minimal generating set of planar moves for surfaces embedded in the four-space

TL;DR

This paper identifies a minimal set of planar moves necessary to manipulate diagrams of surfaces embedded in four-dimensional space, aiding in understanding their topological properties.

Contribution

It introduces a minimal generating set of planar moves for surface diagrams in four-space, simplifying the study of their embeddings.

Findings

Derived a minimal set of moves for surface diagrams

Simplified the process of manipulating surface embeddings

Enhanced understanding of surface topology in four-space

Abstract

We derive a minimal generating set of planar moves for diagrams of surfaces embedded in the four-space. These diagrams appear as the bonded classical unlink diagrams.