Modular Categories

Abstract

• Modular categories serve as input datum for the Reshetikhin-Turaev construction of topological quantum field theories in 2+1 dimensions and therefore give rise to invariants of smooth 3-manifolds. This goes some way towards making Witten’s interpretation of the Jones polynomial via Chern-Simons QFT rigorous. (But since there still is no complete rigorous non-perturbative construction of the Chern-Simons QFTs by conventional quantum field theory methods, there also is no proof of their equivalence to the RT-TQFTs constructed using the representation theory of quantum groups.)