ON THE UNIFICATION OF QUANTUM 3–MANIFOLD INVARIANTS

In 2006 Habiro initiated a construction of generating functions for Witten–Reshetikhin–Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Bühler and Christian Blanchet we extended his construction to a larger class of 3–manifolds. The unified invariants provide a strong tool to study properties of the whole collection of WRT invariants, e.g. their integrality, and hence, their categorification.

In this paper we give a survey on ideas and techniques used in the construction of the unified invariants.