A General Fredholm Theory III: Fredholm Functors and Polyfolds

Details A General Fredholm Theory III: Fredholm Functors and Polyfolds A General Fredholm Theory III: Fredholm Functors and Polyfolds

2008-10-03

arxiv.org/abs/0810.0736v1

Mathematics

Functional Analysis

119 pages, 3 figures

Scientific paper

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.

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