A remark on configuration spaces of two points

TL;DR

This paper establishes a homotopy invariance property for a specific covering space related to the configuration space of two points in a product of a closed manifold and an aspherical space, expanding understanding of configuration spaces.

Contribution

It proves a homotopy invariance result for a covering space of the configuration space of two points in a product involving a closed manifold and an aspherical space, which was previously unexplored.

Findings

Homotopy invariance of a certain covering space established

Results apply to configuration spaces in product manifolds

Advances understanding of topological properties of configuration spaces

Abstract

We prove a homotopy invariance result for a certain covering space of the space of ordered configurations of two points in $M \times X$ where $M$ is a closed smooth manifold and $X$ is any fixed aspherical space which is not a point.