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In this paper we construct Riemannian metrics and weight functions over Casson handles. We show that the corresponding Atiyah-Hitchin-Singer complexes are Fredholm for some class of Casson handles of bounded type. Using these, the Yang-Mills moduli spaces are constructed as finite dimensional smooth manifolds over Casson handles in the class.doi:10.2140/gt.2004.8.779 fatcat:3hw6rbj4hvf67m7xxusktf7enm