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.

arXiv comment72 pages

References in corpus (10)

• Extremal metrics on blow ups
• Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow
• An SO(3)-monopole cobordism formula relating Donaldson and Seiberg-Witten invariants
• Energy gap for Yang-Mills connections, I: Four-dimensional closed Riemannian manifolds
• Donaldson invariants and wall-crossing formulas. I: Continuity of gluing maps
• Applications of Polyfold Theory I: The Polyfolds of Gromov-Witten Theory
• Superconformal simple type and Witten's conjecture
• The SO(3) monopole cobordism and superconformal simple type
• Discreteness for energies of Yang-Mills connections over four-dimensional manifolds
• Manifolds with analytic corners

Cited by in corpus (1)

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