2010/02/17 by Helmut Hofer, Hofer, Helmut, Kris Wysocki +3
Mathematics · #46T05 #46T99 #53C99 #53D40 #53D50 #54CXX #58B99 #58D27 #58J05 #FOS: Mathematics #Functional Analysis (math.FA) #Symplectic Geometry (math.SG) #math.FA #math.SG #msc:46T05 #msc:46T99 #msc:53C99 #msc:53D40 #msc:53D50 #msc:54CXX #msc:58B99 #msc:58D27 #msc:58J05
paper · pdf · doi:10.48550/arxiv.1002.3381
178 pages, 8 figures
arxiv created 2010/02/17 · arxiv updated 2010/02/26
We survey a (nonlinear) Fredholm theory for a new class of ambient spaces called polyfolds, and develop the analytical foundations for some of the applications of the theory. The basic feature of these new spaces, which can be finite and infinite dimensional, 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 like bubbling-off. The theory is applicable to Gromov-Witten and Floer Theory as well as Symplectic Field Theory.