A Reidemeister Theorem for Solid Ribbon Torus Links

TL;DR

This paper extends Reidemeister theory to a new class of four-dimensional links called solid ribbon torus links, providing a complete characterization up to ribbon isotopy.

Contribution

It introduces a Reidemeister Theorem for solid ribbon torus links, a class related to welded links but in four dimensions, filling a gap in topological link theory.

Findings

Reidemeister Theorem established for solid ribbon torus links

Characterization of these links up to ribbon isotopy

Advances understanding of 4D link structures

Abstract

A complete Reidemeister characterisation of welded links is a long-standing open problem. We present a Reidemeister Theorem for a related class of four-dimensional links, solid ribbon torus links: immersed solid tori in R4 with only ribbon singularities, considered up to generalised ribbon isotopy.