Polyfolds And A General Fredholm Theory

Abstract

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

References in corpus (4)

• Compactness results in Symplectic Field Theory
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Orbifolds as Groupoids: an Introduction
• Integration Theory for Zero Sets of Polyfold Fredholm Sections

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• The polyfold--Kuranishi correspondence I: A choice-independent theory of Kuranishi structures
• Source Spaces and Perturbations for Cluster Complexes
• On growth rate and contact homology
• On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification
• Transversality problems in symplectic field theory and a new Fredholm theory
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• Spectral geometry of the group of Hamiltonian symplectomorphisms