On the unification of quantum 3-manifold invariants

TL;DR

This paper surveys the development of unified quantum invariants for 3-manifolds, which encapsulate Witten-Reshetikhin-Turaev invariants and facilitate their study, including integrality and categorification.

Contribution

It reviews the construction and extension of unified WRT invariants for a broad class of 3-manifolds, highlighting their significance in quantum topology.

Findings

Unified invariants encompass WRT invariants for various 3-manifolds.

They enable analysis of integrality and categorification of quantum invariants.

The paper summarizes key ideas and techniques in constructing these invariants.

Abstract

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 Buehler 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.