What is known about the relation of Donaldson invariants on a complex surface $\Sigma$ and GW invariants (or equivalent) of local Calabi-Yau 3folds such as the canonical bundle of $\Sigma$? (if any of course)
I would like to understand any such relation either from a physics or a maths point of view.
Are there any known relations, results, formulae, papers? Any kind of references would be very much appreciated.