分野別セミナー

The gauge group of a principal bundle $P$ is the topological group of automorphisms of $P$. Gauge groups have been intensely studied, but not much is known about the cohomology of their classifying spaces. In this talk, I will talk about the cohomology of the classifying spaces of gauge groups of principal $SO(n)$-bundles over $S^2$. More precisely, we determine the cohomology of the classifying space of the gauge group of the non-trivial principal $SO(n)$-bundle over $S^2$ for $n=3,4$, and then I will show that the cohomology of the classifying space of the gauge group of the non-trivial principal $SO(n)$-bundle over $S^2$ for $n\ge 3$ is torsion free if and only if $n=3,4$. I will also talk about the classification of the homotopy types of the gauge groups of principal $SO(n)$-bundles over a Riemann surface for $n=3,4$.