Sc-Smoothness, Retractions and New Models for Smooth Spaces

By Helmut Hofer, K. Wysocki, E. Zehnder. 2010

68 citations recorded by the source corpus.

We survey a (nonlinear) Fredholm theory for a new class of ambient spaces called polyfolds, and develop the analytical foundations for some of the applications of the theory. The basic feature of these new spaces, which can be finite and infinite dimensional, 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 like bubbling-off. The theory is applicable to Gromov-Witten and Floer Theory as well as Symplectic Field Theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/21fcaee3e721ab26eccdff61ae4a0dff48d65b76

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Polyfold and Fredholm Theory (2014, methodology): “lems in symplectic geometry. In [11] we shall use this approach to deﬁne a Fredholm setup for SFT. The language for doing so is that developed in [29, 30]. The necessary nonlinear analysis comes from [31]. In [10] the ideas described here are carried out on the level of a graduate text describing th”
Bounds on spectral norms and barcodes (2018, background): “ientable, one expects this statement to hold in full generality, with coecients in a eld of characteristic 0;by techniques of virtual fundamental cycles in Hamiltonian Floer theory (see [47, 70, 88],[45, 54, 55, 56], and see also [57, 73] for a recent description of the state of the art and further ”