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arXiv · 1210.6670

Polyfolds: A First and Second Look

Oliver Fabert·Joel W. Fish·Roman Golovko·Katrin Wehrheim
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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.

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Oliver Fabert, Joel W. Fish, Roman Golovko, Katrin Wehrheim. 2012-10-24. Polyfolds: A First and Second Look. https://doi.org/10.4171/emss%2F16

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