A General Fredholm Theory III: Fredholm Functors and Polyfolds

Abstract

We describe a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. The basic feature of these new spaces is that in general they may have locally varying dimensions. These new spaces are needed for a functional analytic treatment of nonlinear problems involving analytic limiting behavior. This theory is applicable to Gromov-Witten and Floer Theory as well as Symplectic Field Theory.

119 pages, 3 figures

References in corpus (6)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Orbifolds as Groupoids: an Introduction
• Integration Theory for Zero Sets of Polyfold Fredholm Sections
• A General Fredholm Theory II: Implicit Function Theorems
• Symplectic hypersurfaces and transversality in Gromov-Witten theory
• A General Fredholm Theory I: A Splicing-Based Differential Geometry

Cited by in corpus (5)

• Complex Path Integrals and the Space of Theories
• Integration Theory for Zero Sets of Polyfold Fredholm Sections
• Correlators and Descendants of Subcritical Stein Manifolds
• Gravitational Descendants and Linearized Contact Homology
• Hamiltonian partial differential equations and symplectic scale manifolds