Homology, Homotopy and Applications

Volume 23 (2021)

Number 1

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

Pages: 17 – 24

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n1.a2


Masahiro Takeda (Department of Mathematics, Kyoto University, Kyoto, Japan)


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.


cohomology, gauge group, classifying space

2010 Mathematics Subject Classification


Received 20 October 2019

Received revised 21 January 2020

Accepted 1 February 2020

Published 5 August 2020