Moduli space of instantons on non-compact manifolds

Question

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

Answer 1

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:

• $L^2$ Moduli Spaces on 4-Manifolds with Cylindrical Ends, Clifford Taubes, International Press, ISBN: 1-57146-007-1.
• Gauge theory on asymptotically periodic $4$-manifolds, Clifford Taubes, J. Differential Geom. Volume 25, Number 3 (1987), 363-430.
• ASD moduli spaces over four-manifolds with tree-like ends, Tsuyoshi Kato, Geom. Topol. 8(2004) 779-830, arXiv:math/0405443v1 [math.GT].

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.