On the number of non-equivalent differentiable structures on 4-manifolds
Recently, by virtue of Donaldson's new invariant, it became possible to construct some algebraic surfaces which are homeomorphic to each other, but not diffeomorphic. The author considers some iterated cyclic coverings of \({\mathbb{P}}^ 2\) so that he could construct such surfaces which are simply connected. He also shows that, for any given value of k, his method realizes k distinct differentiable structures (as complex surfaces) on a single topological 4-manifold. So this implies that the moduli spaces of surfaces with given numerical characters can have arbitrary many connected components.
scientific article; zbMATH DE number 4116703