Polyfold and Fredholm Theory I: Basic Theory in M-Polyfolds
| Autor: | Hofer, Helmut H., Wysocki, Kris, Zehnder, Eduard |
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| Rok vydání: | 2014 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The main topic is the development of a Fredholm theory in a new class of spaces called M-polyfolds. In the subsequent Volume II the theory will be generalized to an even larger class of spaces called polyfolds, which can also incorporate local symmetries. The whole package provides a functional analytic framework to deal with compactness and transversality issues as they occur in moduli problems of symplectic geometry. Applications of the theory cover Floer-type theories as they occur in symplectic geometry. M-polyfolds and the more general polyfolds are smooth spaces which can be finite-dimensional as well as infinite-dimensional. In applications of interest they in general have locally varying dimensions. Despite the fact that the spaces are much more general than Banach manifolds a nonlinear Fredholm theory with the usual features is possible (Sard-Smale type perturbation theory). This generalized Fredholm theory can be applied to classes of nonlinear elliptic problems which show bubbling-off phenomena but allow for certain kind of compactifications. Comment: 246 pages, 7 figures |
| Databáze: | arXiv |
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