Geodesic
A general Fredholm theory I: a splicing-based differential geometry
Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 841-876

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This is the first paper in a series introducing a generalized Fredholm theory in a new class of smooth spaces called polyfolds. These spaces, in general, are locally not homeomorphic to open sets in Banach spaces. The present paper describes some of the differential geometry of this new class of spaces. The theory will be illustrated in upcoming papers by applications to Floer Theory, Gromov-Witten Theory, and Symplectic Field Theory.
DOI : 10.4171/jems/99
Classification : 46-XX, 00-XX, 53-XX, 58-XX
Keywords: Banach scales, sc-smoothness, M-polyfolds, splicings, splicing cores, fillers, strong bundles 
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     author = {Helmut W. Hofer and Kris Wysocki and Eduard Zehnder},
     title = {A general {Fredholm} theory {I:} a splicing-based differential geometry},
     journal = {Journal of the European Mathematical Society},
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     year = {2007},
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}
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Helmut W. Hofer; Kris Wysocki; Eduard Zehnder. A general Fredholm theory I: a splicing-based differential geometry. Journal of the European Mathematical Society, Tome 9 (2007) no. 4, pp. 841-876. doi: 10.4171/jems/99

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