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We study analytic aspects of U(n) gauge theory over a toric noncommutative manifold M θ . We analyse moduli spaces of solutions to the selfdual Yang-Mills equations on U(2) vector bundles over four-manifolds M θ , showing that each such moduli space is either empty or a smooth Hausdorff manifold whose dimension we explicitly compute. In the special case of the four-sphere S 4 θ we find that the moduli space of U(2) instantons with fixed second Chern number k is a smooth manifold of dimension 8kdoi:10.4310/atmp.2013.v17.n5.a5 fatcat:5pdnnf3zvbfuhmmyusuforhwxi