GRASP Seminar: Reshetikhin-Turaev invariants

Seminar | September 26 | 11 a.m.-12 p.m. | 939 Evans Hall

 Aaron Brookner, UCB

 Department of Mathematics

Continuing from last week, we define "universal R-matrices" of Hopf algebras and the braiding structure of categories provided. This defines actions of the braid groups $B_n$ as morphisms of modules. We finally construct the RT invariants, as functors from the tangle category to these, and compute the very simplest examples using two methods. Lastly we provide references to the literature about categorifying some of these notions: there are higher braid groups $T(k,n)$ generalizing $B_n=T(1,n)$, and there are braided monoidal 2-categories.