2 problems

Atiyah–Bott conjecture. The $G$-equivariant index of an elliptic operator can be computed purely in terms of data around the $G$-fixed points.

Let $X$ be a String manifold, so that its loop-space bundle admits a lift of its structure group from $\mathcal{L}\mathrm{Spin}_n$ to its universal central extension. Consider a hy…