Independence of Yoshikawa eighth move and a minimal generating set of band moves

TL;DR

This paper proves the independence of the Yoshikawa eighth move using surface-link groups and establishes a minimal generating set of band moves for links with bands, advancing the understanding of surface-link diagram transformations.

Contribution

It introduces a new proof of the independence of the Yoshikawa eighth move and identifies a minimal generating set of band moves for links with bands.

Findings

Proves the independence of the Yoshikawa eighth move.

Establishes a minimal generating set of band moves for links with bands.

Uses surface-link group of a mirror cut surface in the proof.

Abstract

Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mirror cut surface. By using a surface-link group of a mirror cut surface of a twisted diagram we will prove the independence of Yoshikawa eighth move. As a consequence we will establish a minimal generating set of band moves for links with bands.