Everything around sl(2+,\eps) is DoPeGDO. So what?

Dror Bar-Natan – 23 October 2019

I'll explain what "everything around" means: the classical and quantum product, co-product, antipode, trace, R-matrix, cuap, and Cartan involution, as well as the dual pairing, the associator, the twist element, the dequantizator, and more, and all of their compositions. What DoPeGDO means: the category of Docile Perturbed Gaussian Differential Operators. And what sl(2+,\eps) means: a solvable approximation of the semi-simple Lie algebra sl(2).

Knot theorists should rejoice because all this leads to very powerful and well-behaved poly-time-computable knot invariants. Quantum algebraists should rejoice because it's a realistic playground for testing complicated equations and theories.

This is joint work with Roland van der Veen and continues work by Rozansky and Overbay.