Polyfolds And A General Fredholm Theory

Details Polyfolds And A General Fredholm Theory Polyfolds And A General Fredholm Theory

2008-09-22

arxiv.org/abs/0809.3753v1

Mathematics

Symplectic Geometry

57 pages, 1 figure

Scientific paper

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.

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