# Cohomology of the classifying spaces of $U(n)$-gauge groups over the 2-sphere

## TL;DR

This paper computes the integral cohomology ring of classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere, extending methods involving free double suspension to this context.

## Contribution

It introduces a generalization of the free double suspension operation to compute the cohomology of gauge group classifying spaces over the 2-sphere.

## Key findings

- Computed the integral cohomology ring explicitly.
- Extended the free double suspension technique.
- Provided new insights into gauge group topology.

## Abstract

A gauge group is the topological group of automorphisms of a principal bundle. We compute the integral cohomology ring of the classifying spaces of gauge groups of principal U(n)-bundles over the 2-sphere by generalizing the operation for free loop spaces, called the free double suspension.