ASD moduli spaces over four-manifolds with tree-like ends (Q1882833)

The author constructs Riemannian metrics and weight functions over Casson handles. His main result is that when \(S\) is a smooth oriented open 4-manifold constructed by attaching to a zero handle Casson handles of homogeneous trees of bounded type, then there exists a complete Riemannian metric of bounded geometry \(g\) and a weight function \(w\) on \(S\) such that one can construct ASD moduli spaces over \(S\) as finite dimensional smooth manifolds with respect to \((S,g,w).\) The issue of perturbation theory on Casson handles still unresolved.