Polyfolds: A First and Second Look
Abstract
Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves. It aims to systematically address the common difficulties of compactification and transversality with a new notion of smoothness on Banach spaces, new local models for differential geometry, and a nonlinear Fredholm theory in the new context. We shine meta-mathematical light on the bigger picture and core ideas of this theory. In addition, we compiled and condensed the core definitions and theorems of polyfold theory into a streamlined exposition, and outline their application at the example of Morse theory.
Cite
@article{arxiv.1210.6670,
title = {Polyfolds: A First and Second Look},
author = {Oliver Fabert and Joel W. Fish and Roman Golovko and Katrin Wehrheim},
journal= {arXiv preprint arXiv:1210.6670},
year = {2016}
}
Comments
62 pages, 2 figures. Example 2.1.3 has been modified. Final version, to appear in the EMS Surv. Math. Sci