Are there any references about the moduli space of instantons on a general non-compact manifold?
Moduli space of instantons on non-compact manifolds
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differential-geometry
gauge-theory
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0Yes. Or no. If you want a better responce, ask a better question. http://math.stackexchange.com/faq – 2012-06-20
1 Answers
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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:
- $L^2$ 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.
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1Four 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