Has anybody done computations of such a theory? Is there a place I could look up and see what the answers are for low crossing knots?
Slava Krushkal and I have an alternative approach set inside of Dror Bar-Natan's universal construction. It should agree with results obtained by Webster and Frenkel, Stroppel Sussan. Computations are reasonable in our setting. We hope to place the paper on the arxiv shortly.
I did some calculations, but they are hard. Already for the unknot one gets an interesting, but infinite complex with cohomologies in all degrees!
We are just finishing a paper on this which hopefully will appear at the end of next week. Are there any specific knots you are interested in?