All of the other diagrammatic calculi I know of can be utilised with basically just combinatorial knowledge - for instance calculating knot and link polynomials. Are there similar combinatorial invariants like a link polynomial equivalent for Kirby calculus?
If there's a paper or book presenting Kirby calculus from a combinatorial angle can you please provide a reference. If not can you give me an idea of why this is not interesting (i.e. no-one has investigated it).
Thank you.
Can you precise what you mean by Kirby calculus and combinatorial angle? Because there exist invariants of 3 manifolds build on a surgery presentation using skein theory (which is combinatory) and which are invariant under the kirby moves see "Three-manifold invariants derived from the Kauffman bracket" by C Blanchet, N Habegger, G Masbaum, P Vogel . But I don't know if this is an answer to your question...