A general Fredholm theory III: Fredholm functors and polyfolds

A General Fredholm Theory III: Fredholm Functors and Polyfolds

2 Ep-Groupoids and Generalized Maps 17 2.1 Ep-Groupoids . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Functors and Equivalences . . . . . . . . . . . . . . . . . . . . 21 2.3 Inversion of Equivalences and Generalized Maps . . . . . . . . 28 2.4 Strong Bundles over Ep-Groupoids . . . . . . . . . . . . . . . 33 2.5 Auxiliary Norms . . . . . . . . . . . . . . . . . . . . . . . . . 4...

Polyfolds And A General Fredholm Theory

A General Fredholm Theory and Applications

The theory described here results from an attempt to find a general abstract framework in which various theories, like Gromov-Witten Theory (GW), Floer Theory (FT), Contact Homology (CH) and more generally Symplectic Field Theory (SFT) can be understood from a general point of view. Let us describe the general landscape in a somewhat oversimplified form. The common feature (with the exception o...

A General Fredholm Theory I: A Splicing-Based Differential Geometry

1 Introduction In a series of papers we develop a generalized Fredholm theory and demonstrate its applicability to a variety of problems including Floer theory, Gromov-Witten theory, contact homology, and symplectic field theory. Here are some of the basic common features: • The moduli spaces are solutions of elliptic PDE's showing serious non-compactness phenomena having well-known names like ...

A General Fredholm Theory II: Implicit Function Theorems