Superposition of configurations and scanning

TL;DR

This paper introduces a new product structure on the cohomology of configuration spaces of manifolds, linking it to the cup-product via the scanning isomorphism, thus providing a novel algebraic perspective.

Contribution

It establishes a correspondence between a superposition product on configuration space cohomology and the cup-product in section spaces through the scanning isomorphism.

Findings

The superposition product aligns with the cup-product under the scanning isomorphism.

Provides a new algebraic structure on configuration space cohomology.

Bridges geometric configurations with algebraic topology via the scanning map.

Abstract

We endow the cohomology of configuration spaces of a manifold with a product arising from superposing configurations. We prove that, under the scanning isomorphism, this product corresponds to the cup-product of the section space of the standard scanning bundle of the manifold.