A general Fredholm theory III: Fredholm functors and polyfolds

Hofer, Helmut¹ ; Wysocki, Kris² ; Zehnder, Eduard³

¹ Courant Institute, New York University, 251 Mercer Street, New York, 10012, USA
² Mathematics Department, Penn State University, University Park, State College, PA 16802, USA
³ Department of Mathematik, ETH-Zentrum, CH 8092 Zürich, Switzerland

Geometry & topology, Tome 13 (2009) no. 4, pp. 2279-2387.

Résumé

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 Fredholm theory, which for M–polyfolds has been presented in our paper [Geom. Funct. Anal. 18 (2009)], to the more general polyfold setting. The Fredholm theory consists of a transversality and a perturbation theory. The results form the basis for our application to Symplectic Field Theory.

Détail

DOI : 10.2140/gt.2009.13.2279

Keywords: ep-groupoid, polyfold, branched suborbifold, strong polyfold bundle, Fredholm section of polyfold bundle

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