Categorification: tangle invariants and TQFTs
Abstract
Based on different views on the Jones polynomial we review representation theoretic categorified link and tangle invariants. We unify them in a common combinatorial framework and connect them via the theory of Soergel bimodules. The influence of these categorifications on the development of 2representation theory and the interaction between topological invariants and 2categorical structures is discussed. Finally, we indicate how categorified representations of quantum groups on the one hand and monoidal 2categories of Soergel bimodules on the other hand might lead to new interesting 4dimensional TQFTs.
 Publication:

arXiv eprints
 Pub Date:
 July 2022
 arXiv:
 arXiv:2207.05139
 Bibcode:
 2022arXiv220705139S
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  General Topology;
 Mathematics  Representation Theory;
 17B10;
 17B37;
 57M27;
 18E10;
 57R56;
 05A30;
 37F20
 EPrint:
 To appear in Proceedings of the ICM 2022. The ICM talk addresses Conjecture 3.8 and formulates the crucial main theorem which allows to settle this conjecture