This paper determines the integral cohomology ring of classifying spaces of U(n)-gauge groups over the 2-sphere for every Chern number k.
Kaji, Low rank cohomology of the classifying spaces of gauge groups over 3-manifolds
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Cohomology of the classifying spaces of $U(n)$-gauge groups over the 2-sphere
This paper determines the integral cohomology ring of classifying spaces of U(n)-gauge groups over the 2-sphere for every Chern number k.