Mathematics

Freedman's Theorem in classification theory gives the classification of simply connected smooth manifolds up to homeomorphism via intersection forms. However the classification of four manifolds up to diffeomorphism is entirely a new story due to the fact that most of the machinery used to classify spaces in dimension higher then four failed in dimension four. For example dimension four is the only dimension where one finds the manifolds which are homeomorphic to R^4 but not diffeomorphic to it. This led Donaldson to define a new set on invariants called the Donaldson invariants. These invariants are defined by studying the moduli spaces of ASD-connections.In this seminar I will explain the structure over such moduli spaces and we will define the Donaldson invariants when the moduli space has zero dimension, called zero dimensional Donaldson invariants.