  We describe a new approach to the problem of constructing gluing
parameterizations for open neighborhoods of boundary points of moduli spaces of
anti-self-dual connections over closed four-dimensional manifolds. Our approach
employs general results from differential topology for $C^1$ maps of smooth
Banach manifolds with corners, providing a method that should apply to other
problems in geometric analysis involving the gluing construction of solutions
to nonlinear partial differential equations.
