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Are there any references about the moduli space of instantons on a general non-compact manifold?

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Yes. Or no. If you want a better responce, ask a better question. – Gunnar Þór Magnússon Jun 20 '12 at 23:41
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I don't know of any work on Donaldson theory on general non-compact manifolds, but if you assume the manifold is nicely behaved "at infinity," there are some references:

The special restriction on the asymptotic behavior of the manifold is apparent in the title of each respective work; see the references for precise definitions.

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Thanks a lot. These are exactly the kind of stuff I was looking for. – Moduli Jun 21 '12 at 2:12

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