In the late 1990's, Khovanov discovered an interesting cohomological invariant of links. It can be seen as a "categorification" of the Jones polynomial. For any link diagram D, Khovanov gives a combinatorially constructed cochain complex of graded vector spaces. The cohomology of this cochain complex is known as Khovanov homology. I will begin my talk by providing some motivation for Khovanov homology, proceed to discus the Jones polynomial and Khovanov homology (with some examples and proofs depending on time), and then state and prove a general formula for the Khovanov homology of (2,n) Torus knots.
The talk should be accessible to everybody (elementary algebra required).