A General Fredholm Theory II: Implicit Function Theorems

By Helmut Hofer, K. Wysocki, E. Zehnder. 2007

105 citations recorded by the source corpus.

Abstract.This is the second paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. In general, these spaces are not locally homeomorphic to open sets in Banach spaces. The current paper develops the Fredholm theory in M-polyfold bundles. It consists of a transversality and a perturbation theory. In upcoming papers the generalized Fredholm theory will be applied to the Floer Theory, the Gromov–Witten Theory and the Symplectic Field Theory

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/27a1b02c43552f48e714118b7c9bbaa5d3ea7093

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In Mathematical Physics

Citations in the corpus

Effect of Legendrian surgery (2009, methodology): “However for the purposes of this exposition we ignore this difficulty and claim that the correct version can be built according to the scheme presented here using one of the, for this purpose, currently developed technologies, notably, the polyfold theory of H Hofer, K Wysocki, and E Zehnder [31; 32”
Polyfold and Fredholm Theory (2014, background): “An sc-Fredholm section according to the above definition is slightly more general than the sc-Fredholm sections defined in [25].”
$S^1$-equivariant symplectic homology and linearized contact homology (2012, methodology): “nt linearized contact homology groups. These groups depend a priori on the choice of α,J,f,g and the proof of invariance with respect to these choices should again be a consequence of polyfold theory [38, 39, 40, 41]. For readability we denote them by NCHlin ∗ (M), respectively NCHlin ∗ (M). The exa”
A general Fredholm theory III: Fredholm functors and polyfolds (2008, methodology): “For the the definition of the m-convergence we refer to [26].”
Disk enumeration on the quintic 3-fold (2006, background): “me the coordinate transforms and Kuranishi maps are smooth, as explained in [3, Appendix A1.4]. We anticipate that with the completion of the generalized Fredholm theory currently being introduced in [8, 9], the ideas of Section 5.2-5.3 will translate into a proof of Theorem 3 based on that framewor”
Sc-Smoothness, Retractions and New Models for Smooth Spaces (2010, background): “If, in addition, the linearization f (x) : TxX → Wx is surjective, then our implicit function theorem gives a natural smooth structure on the solution set of f(y) = 0 near x as the following theorem from [10] shows.”