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A General Fredholm Theory III: Fredholm Functors and Polyfolds

2008/10/03 by Helmut Hofer, Hofer, Helmut, Kris Wysocki +3
Mathematics · #46T05 #46T99 #53C99 #53D40 #53D50 #54CXX #58B99 #58D27 #58J05 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #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.0810.0736

119 pages, 3 figures

arxiv created 2008/10/03 · openalex publication_date 2008/10/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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