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moduli space of flat bundles
Posted:
Feb 14, 2006 9:13 AM


I believe it's true that for any connected smooth manifold M and Lie group G, the "moduli space of flat Gbundles" over M is
hom(pi_1(M),G)/G
where pi_1(M) is the fundamental group of M, and G acts on the homomorphisms from pi_1(M) to G by conjugation.
However, when I seek references for this fact, I'm always led to Narisimhan and Seshadri's paper where they prove this when M is a Riemann surface (and maybe in the analytic or algebraic rather than smooth context).
So, is my belief true? And, almost more importantly: what's a good reference???



