Andreas Stavrou: Superposition of configurations and scanning

Abstract

It is known that “scanning” provides an isomorphism between the cohomologies of all configuration spaces of a manifold and the cohomology of the section space of a certain bundle over the manifold. Of course, under this isomorphism, the cup product of the section space naturally gives a product on the cohomologies of configuration spaces. Surprisingly, this product also arises independently from the scanning isomorphism via “superposition of configurations”. In this talk, I will define the “superposition product” and sketch the proof that under the scanning isomorphism it corresponds to the cup product of the section space.