### ASD moduli spaces over four-manifolds with tree-like ends.

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We describe alternate methods of solution for a model arising in the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory and provide a complete argument for the characterization put forth by Argyres, Faraggi, and Shapere of the curve $Im{a}_{D}/a=0$.

Let $M$ a compact connected oriented 4-manifold. We study the space $\Xi $ of ${\mathrm{Spin}}^{\mathrm{c}}$-structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on $M$. In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all ${\mathrm{Spin}}^{\mathrm{c}}$-structures $\Xi $. We prove that, on a complex Kähler surface, for an hermitian metric $h$ sufficiently close to the original Kähler metric, the moduli space...