A General Fredholm Theory III: Fredholm Functors and Polyfolds
  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. 
Helmut Hofer, Kris Wysocki and Eduard Zehnder