Invariants of Knots and 3-manifolds from Quantum Groupoids

TL;DR

This paper develops new invariants for knots and 3-manifolds using categories derived from finite dimensional quantum groupoids, expanding the toolkit for topological quantum field theory.

Contribution

It introduces a novel approach to constructing knot and 3-manifold invariants via representation categories of quantum groupoids, generalizing existing quantum group methods.

Findings

Constructed ribbon and modular categories from quantum groupoids.

Produced new invariants for knots and 3-manifolds.

Extended the framework of quantum invariants beyond traditional quantum groups.

Abstract

We use categories of representations of finite dimensional quantum groupoids (weak Hopf algebras) to construct ribbon and modular categories that give rise to invariants of knots and 3-manifolds.