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Dec 6, 2010 at 17:20 comment added Malte Wandel thanks. this is more or less what I expected. by now I found an elementary prove by Atiyah himself in Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc. 85 (1957), 181–207, proposition 12. this is what I was actually looking for. but thank you anyway for the reference from caldararu. it's a really nice paper.
Dec 1, 2010 at 16:56 vote accept Malte Wandel
Dec 1, 2010 at 15:21 history answered Leo Alonso CC BY-SA 2.5