University of Sydney Algebra Seminar

Dror Bar-Natan (University of Toronto)

Friday 18 August, 12-1pm, Place: Carslaw 375

The Dogma is Wrong

It has long been known that there are knot invariants associated to semi-simple Lie algebras, and there has long been a dogma as for how to extract them: "quantize and use representation theory". We present an alternative and better procedure: "centrally extend, approximate by solvable, and learn how to re-order exponentials in a universal enveloping algebra". While equivalent to the old invariants via a complicated process, our invariants are in practice stronger, faster to compute (poly-time vs. exp-time), and clearly carry topological information. This is joint work with Roland van der Veen and continues work by Rozansky and Overbay.