20250725 Pjotr Vugts

In this talk we define and give an example of the Khovanov homology, an invariant of knots which is a categorification of the Jones polynomial.

After a quick recap of some necessary knot theory, we will discuss the Jones polynomial. Then we move to the Khovanov bracket, a chain complex in the (additive closure of the Ab-enriched) category of cobordisms. Applying a TQFT to this Khovanov bracket gives us a chain complex of graded abelian groups, with graded Euler characteristic equal to the Jones polynomial. We show that the homology of this complex (this is the Khovanov homology) is a strictly stronger invariant than the Jones polynomial.