On the Donaldson polynomials of elliptic surfaces
The Donaldson invariants of smooth simply connected minimal elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\) are polynomials in the intersection form \(q\) and canonical class \(k\). We compute, using Donaldson-Floer theory, the second nonzero coefficient in their expansion in \(q\) and \(k\) when the geometric genus is odd. We point out how this result (recently obtained also by Morgan and Mrowka, using different methods, for any geometric genus) yields the classification of smooth simply connected elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\) up to diffeomorphism.
classification of smooth simply connected elliptic surfaces over \(\mathbb{C} \mathbb{P}^ 1\)
Donaldson invariants of smooth simply connected minimal elliptic surfaces
scientific article; zbMATH DE number 683118