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## Seminars

### On the cohomology of the classifying space of $SO(n)$-gauge groups over $S^2$

- Hold Date
- 2023-01-20 16:00〜2023-01-20 17:00
- Place
- room C-616
- Object person
- Speaker
- Yuki Minowa (Kyoto University)

Abstract: 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 $n=3,4$.