Members’ Seminar

Most known smoothable simply connected 4--manifolds admit infinitely many different smooth structures (distinguished, for example, by Seiberg--Witten invariants). There are some 4--manifolds, though, for which the existence of such 'exotic' structures is still open, the most notable examples being the 4--dimensional sphere S^4 and the complex projective plane CP^2. In a recent project with Z. Szabo and J. Park we found constructions of exotic smooth structures on the five- and six-fold blow--up of CP^2. In the lecture we describe the construction of these 4--manifolds and indicate the necessary input from Seiberg--Witten theory for proving their exoticness.