Sc-smoothness, retractions and new models for smooth spaces

Helmut Hofer; Kris Wysocki; Eduard Zehnder

doi:10.3934/dcds.2010.28.665

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2010, Volume 28, Issue 2: 665-788. Doi: 10.3934/dcds.2010.28.665 open access

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Sc-smoothness, retractions and new models for smooth spaces

1.
Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540
2.
Department of Mathematics, Penn State University, State College, PA 16802
3.
Department of Mathematics, ETH Zürich, 8092 Zürich

Received: January 31, 2010

Revised: March 31, 2010

Published: June 2010

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Abstract

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:

sc-Banach spaces,
sc-smoothness,
sc-retraction,
M-polyfold,
sc-Fredholm section of M-polyfold bundle.

Mathematics Subject Classification: Primary: 58B99; Secondary: 58C99.

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