2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170723We 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 figuresFunctional AnalysisSymplectic Geometry46T05,46T99, 53C99, 53D50,53D40,54CXX,58B99, 58D27,58J05text