Modular Categories and TQFTs Beyond Semisimplicity
Abstract
Vladimir Turaev discovered in the early years of quantum topology that the notion of modular category was an appropriate structure for building 3-dimensional Topological Quantum Field Theories (TQFTs for short) containing invariants of links in 3-manifolds such as Witten-Reshetikhin-Turaev ones. In recent years, generalized notions of modular categories, which relax the semisimplicity requirement, have been successfully used to extend Turaev's construction to various non-semisimple settings. We report on these recent developments in the domain, showing the richness of Vladimir's lineage.
Cite
@article{arxiv.2011.12932,
title = {Modular Categories and TQFTs Beyond Semisimplicity},
author = {Christian Blanchet and Marco De Renzi},
journal= {arXiv preprint arXiv:2011.12932},
year = {2022}
}
Comments
26 pages, to appear in Topology and Geometry: A Collection of Essays Dedicated to Vladimir G. Turaev, ed. A. Papadopoulos, European Mathematical Society Publishing House, Berlin, 2021. Formulas for semisimple stabilization coefficients fixed in version 2