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Topic: moduli space of flat bundles
Replies: 3   Last Post: Feb 25, 2006 10:00 AM

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John Baez

Posts: 542
Registered: 12/6/04
moduli space of flat bundles
Posted: Feb 14, 2006 9:13 AM
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I believe it's true that for any connected smooth manifold M
and Lie group G, the "moduli space of flat G-bundles" 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???




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