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June  2010, 28(2): 665-788. doi: 10.3934/dcds.2010.28.665

Sc-smoothness, retractions and new models for smooth spaces

Helmut Hofer 1, , Kris Wysocki 2, and  Eduard Zehnder 3,

1. 

Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, United States
2. 

Department of Mathematics, Penn State University, State College, PA 16802, United States
3. 

Department of Mathematics, ETH Zürich, 8092 Zürich, United States

Received  February 2010 Revised  April 2010 Published  April 2010

We present the concept of sc-smoothness for Banach spaces, which leads to new models of spaces having locally varying dimensions called M-polyfolds. We present detailed proofs of the technical results needed for the applications, in particular, to the Symplectic Field Theory. We also outline a very general Fredholm theory for bundles over M-polyfolds. The concepts are illustrated by holomorphic mappings between conformal cylinders which break apart as the modulus tends to infinity.
Keywords: M-polyfold, sc-Fredholm section of M-polyfold bundle., sc-retraction, sc-Banach spaces, sc-smoothness.
Mathematics Subject Classification: Primary: 58B99; Secondary: 58C9.
Citation: Helmut Hofer, Kris Wysocki, Eduard Zehnder. Sc-smoothness, retractions and new models for smooth spaces. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 665-788. doi: 10.3934/dcds.2010.28.665
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