Abstract:

We offer a gentle introduction to the theory of Khovanov homology of links in R^3. We start from link diagrams and Reidemeister moves, then we define Kauffman bracket invariant (a framed version of the Jones polynomial) and illustrate its basic property. Khovanov homology categorifies the Jones polynomial; we show how Hochschild homology of algebras (truncated polynomials in this case) can be used to introduce Khovanov homology. The deep theory of Hochschild homology and related Connes cyclic homology illuminates the foundation of Khovanov theory.