Volume 13, issue 4 (2009)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A general Fredholm theory III: Fredholm functors and polyfolds

Helmut Hofer, Kris Wysocki and Eduard Zehnder

Geometry & Topology 13 (2009) 2279–2387
Abstract

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.

Keywords
ep-groupoid, polyfold, branched suborbifold, strong polyfold bundle, Fredholm section of polyfold bundle
Mathematical Subject Classification 2000
Primary: 58B99, 58C99
Secondary: 46T99, 57R17
References
Publication
Received: 4 October 2008
Accepted: 22 April 2009
Published: 4 June 2009
Proposed: Leonid Polterovich
Seconded: Yasha Eliashberg, Danny Calegari
Authors
Helmut Hofer
Courant Institute
New York University
251 Mercer Street
New York, 10012
USA
Kris Wysocki
Mathematics Department
Penn State University
University Park
State College, PA 16802
USA
Eduard Zehnder
Department of Mathematik
ETH-Zentrum
CH 8092 Zürich
Switzerland