Polyfolds And A General Fredholm Theory
Polyfolds And A General Fredholm Theory
We survey a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. This theory is being currently developed jointly with K. Wysocki and E. Zehnder. 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.
57 pages, 1 figure
- New York University United States
Mathematics - Functional Analysis, 46T05,46T99, 53C99, 53D50,53D40,54CXX,58B99, 58D27,58J05, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Functional Analysis (math.FA)
Mathematics - Functional Analysis, 46T05,46T99, 53C99, 53D50,53D40,54CXX,58B99, 58D27,58J05, Mathematics - Symplectic Geometry, FOS: Mathematics, Symplectic Geometry (math.SG), Functional Analysis (math.FA)
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