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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. http://math.stackexchange.com/faq2012-06-20

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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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    Four years later, but: Morgan-Mrowka-Ruberman is also worth noting; more or less an alternate approach to the ideas in Taubes' book.2016-07-12