2008/09/22 by Helmut Hofer, Hofer, Helmut · 2 citations
Mathematics · #46T05 #46T99 #53C99 #53D40 #53D50 #54CXX #58B99 #58D27 #58J05 #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.0809.3753
openalex publication_date 2008/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.