A general Fredholm theory III: Fredholm functors and polyfolds

Abstract

This is the third in a series of papers devoted to a general Fredholm theory in a new class of spaces, called polyfolds. We first introduce ep–groupoids and polyfolds. Then we generalize the Fredholm theory, which for M–polyfolds has been presented in our paper [Geom. Funct. Anal. 18 (2009)], to the more general polyfold setting. The Fredholm theory consists of a transversality and a perturbation theory. The results form the basis for our application to Symplectic Field Theory.