I recently finished a seminar going through Atiyah and Bott's paper ''The Yang-Mills Equations over Riemann surfaces''. The ideas going into the proof were surprising and very beautiful to me.

However, beyond its proof's beauty, I'm having trouble seeing the use of what I've just read. For instance, as I understand it the main result of the paper is an inductive formula for the cohomology of the space $\mathcal{C}(n,k)$ (the holomorphic vector bundles of rank $n$ and Chern class $k$ over Riemann surface $M$). This makes what the $\mathcal{C}$ look like a little clearer to me, but I've heard that if $g(M)\ne 0,1$ no very explicit of the $\mathcal{C}$ are known, so the only application I can think of (helping obtain an explicit description of the $\mathcal{C}$) seems not to have worked yet.

That naive train of thought lead me to ask:

What subsequent mathematics has heavily used the results of the Atiyah-Bott paper? Or, more petulantly, what's the point of the result?

(I know that there was a lot of activity on the Yang-Mills ideas which appear in the proof by Donaldson etc., but I'm asking about more direct applications as opposed to something like that.)