# American Institute of Mathematical Sciences

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

## Sc-smoothness, retractions and new models for smooth spaces

 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.
Citation: Helmut Hofer, Kris Wysocki, Eduard Zehnder. Sc-smoothness, retractions and new models for smooth spaces. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 665-788. doi: 10.3934/dcds.2010.28.665
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