a proper (i.e. non-stupid) generalization of the Conway polynomial to some multi-variable polynomial for links seems to be something people are after
How about this:
- Sergey A. Melikhov, Colored finite type invariants and a multi-variable analogue of the Conway polynomial, https://arxiv.org/abs/math/0312007
What is the Conway polynomial supposed to be measuring?
Cochran, Levine and others gave various good answers - see references in the linked paper. Thinking of what the multi-variable Conway polynomial is measuring seems to give a much clearer picture, at least in the 2-variable case. What is less clear is why it does so - I mean that there should be more conceptual proofs.
