Journal of the European Mathematical Society
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A general Fredholm theory I: a splicing-based differential geometryDavid Geraghty, Kris Wysocki and Eduard Zehnder (1) School of Mathematics, Institute for Advanced Study, Einstein Drive, NJ 08540, PRINCETON, UNITED STATES
(2) Department of Mathematics, Penn State University, PA 16802, UNIVERSITY PARK, UNITED STATES
(3) Departement Mathematik, ETH Zürich, LEO D 3, Leonhardstrasse 27, 8092, 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.
Keywords: Banach scales, sc-smoothness, M-polyfolds, splicings, splicing cores, fillers, strong bundles
Geraghty D, Wysocki K, Zehnder E. A general Fredholm theory I: a splicing-based differential geometry. J. Eur. Math. Soc. 9 (2007), 841-876. doi: 10.4171/JEMS/99