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We describe a new approach to the problem of constructing gluingparameterizations for open neighborhoods of boundary points of moduli spaces ofanti-self-dual connections over closed four-dimensional manifolds. Our approachemploys general results from differential topology for $C^1$ maps of smoothBanach manifolds with corners, providing a method that should apply to otherproblems in geometric analysis involving the gluing construction of solutionsto nonlinear partial differential equations.

Gluing in geometric analysis via maps of Banach manifolds with corners and applications to gauge theory