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

Abstract

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.

72 pages

References in corpus (1)

• Discreteness for energies of Yang-Mills connections over four-dimensional manifolds

Cited by in corpus (1)

• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds