I'm an undergraduate student, interested in the low dimensional topology, in particular, the 4-manifold theory. I have a question.

In the knot theory, the Reidemeister moves play fundamental roles. For instance, to prove the fact that the Jones polynomial is an invariant of knots, we can use the Reidemeister moves.

On the other hand, in the 4-manifold theory, there is the Kirby calculus, which play roles similar to the Reidemeister moves.

So, are there some studies about construction of an invariant of 4-manifolds by using the Kirby calculus?

Thanks for your help.