A general Fredholm theory I: A splicing-based differential geometry

@article{Hofer2006AGF,
  title={A general Fredholm theory I: A splicing-based differential geometry},
  author={Helmut H. Hofer and Kris Wysocki and Eduard Zehnder},
  journal={Journal of the European Mathematical Society},
  year={2006},
  volume={9},
  pages={841-876}
}
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 
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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 openExpand
A general Fredholm theory III: Fredholm functors and polyfolds
This is the third in a series of papers devoted to a general Fredholm theory in a new class of spaces, called polyfolds. We first introduce ep–groupoids and polyfolds. Then we generalize the FredholmExpand
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