Mini cours
Khovanov homology Abstract
We will present a construction of Khovanov's complex and of the homotopy
equivalences corresponding to Reidemeister moves. We will introduce the
version which allows us to study the slice genus of knots, and
Rasmussen's prove of Milnor's conjecture on the slice genus of torus
knots will be given. Finally, we will examine constructions for other quantum invariants:
sl(3) Khovanov theory and Khovanov-Rozansky sl(N) theory.
We will finish with a new construction of a categorification of sl(N)
quantum invariant based on trivalent TQFT.