A general Fredholm theory I: a splicing-based differential geometry
Helmut W. HoferInstitute for Advanced Study, Princeton, USA
Kris WysockiPenn State University, University Park, United States
Eduard ZehnderETH Zürich, Switzerland
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.
Cite this article
Helmut W. Hofer, Kris Wysocki, Eduard Zehnder, A general Fredholm theory I: a splicing-based differential geometry. J. Eur. Math. Soc. 9 (2007), no. 4, pp. 841–876DOI 10.4171/JEMS/99