Name: Sc-smoothness, retractions and new models for smooth spaces
Keywords: M-polyfold; Sc-Fredholm section of M-polyfold bundle; Sc-reatraction; Sc-Banach; Sc-Banach spaces; Sc-smoothmess, M-polyfold, 58B99, 53D40, 53D50, 46T05, 54CXX, Sc-smoothmess, 46T99, 53C99

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2010Embargo end date: 01 Jan 2010 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete & Continuous Dynamical Systems - A, volume 28, pages 665-788 (issn: 1553-5231,

Copyright policy )Funded by:NSF | Contact and Symplectic St..., NSF | Pseudoholomorphic Curves ..., NSF | Polyfolds, Fredholm Theor...

Authors: Hofer, Helmut; Wysocki, Kris; Zehnder, Eduard;

doi: 10.3934/dcds.2010.28.665 , 10.3929/ethz-b-000018060 , 10.48550/arxiv.1002.3381

arXiv: 1002.3381

handle: 20.500.11850/18060

Sc-smoothness, retractions and new models for smooth spaces

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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.

Discrete and Continuous Dynamical Systems. Series A, 28 (2)

ISSN:1078-0947

ISSN:1553-5231

Related Organizations

ETH Zurich
Switzerland
Pennsylvania State University
United States
Institute for Advanced Study
United States
New York University
United States

Keywords

M-polyfold; Sc-Fredholm section of M-polyfold bundle; Sc-reatraction; Sc-Banach; Sc-Banach spaces; Sc-smoothmess, M-polyfold, 58B99, 53D40, 53D50, 46T05, 54CXX, Sc-smoothmess, 46T99, 53C99, 58D27, 46T05; 46T99; 53C99; 53D50; 53D40; 54CXX; 58B99; 58D27; 58J05, Functional Analysis (math.FA), Mathematics - Functional Analysis, 58J05, Sc-Banach, Sc-reatraction, Mathematics - Symplectic Geometry, FOS: Mathematics, Sc-Banach spaces, Symplectic Geometry (math.SG), Sc-Fredholm section of M-polyfold bundle

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