The Khovanov homology of L is then defined as the homology H(L) of this complex C(D). It turns out that the Khovanov homology is indeed an invariant of L, and does not depend on the choice of diagram. The graded Euler characteristic of H(L) turns out to be the Jones polynomial of L. However, H(L) has been shown to contain more information about L than the Jones polynomial, but the exact details are not yet fully understood.
In 2006 Dror Bar-Natan developed a computer program to efficiently calculate the Khovanov homology (or category) for any knot.
Read more about Khovanov Homology: Related Theories, The Relation To Link(knot) Polynomials, Applications