Cyclic sets from ribbon string links

TL;DR

This paper constructs cyclic and cocyclic structures on the set of ribbon string links and relates them to quantum invariants via ribbon categories, advancing the understanding of their algebraic and topological properties.

Contribution

It introduces cyclic and cocyclic structures on ribbon string links and connects these to quantum invariants through the framework of ribbon categories.

Findings

Established cyclic and cocyclic set structures on ribbon string links.

Linked these structures to the coend of ribbon categories.

Connected the structures with Reshetikhin-Turaev quantum invariants.

Abstract

In this paper, we first endow the set of ribbon string links (up to isotopy) with a structure of a cyclic and of a cocyclic set. Next, we relate these (co)cyclic sets with those associated with the coend of a ribbon category. The relationship is given by the universal quantum invariants \`a la Reshetikhin-Turaev.