Rational blow-down and small exotic 4-manifolds

Argomento: Geometria

Abstract:
It is known that most simply connected 4-manifolds admit infinitely many "exotic" smooth structures, but the existence of such structures is still unknown for S^4 and CP^2.  We report on the current state of art of exotic structures on rational surfaces, and review how such structures can be constructed. The main ingredients are the rational blow-down process and the computation of appropriate Seiberg-Witten
invariants. We also discuss the classification of plumbing trees which can be symplectically blown down.