7
votes
3answers
567 views

The classifying space of a gauge group

Let $G$ be a Lie group and $P \to M$ a principal $G$-bundle over a closed Riemann surface. The gauge group $\mathcal{G}$ is defined by $$\mathcal{G}=\lbrace f : P \to G \mid f(p \cdot g) = ...
3
votes
1answer
441 views

The number of simply connected 4-dimension manifold

For a simply connected four-dimension manifold, we know the Freedmen's work. My question is: For every integer N, Is the number of simply connected 4-manifolds which the second betti number is ...