Polyfolds: A first and second look

O. Fabert, Joel Fish, Roman Golovko, Katrin Wehrheim

Research output: Contribution to JournalArticleAcademicpeer-review


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.
Original languageEnglish
Article numberDOI: 10.4171/EMSS/16
Pages (from-to)131–208
Number of pages78
JournalEMS Surveys in Mathematical Sciences
Issue number2
Publication statusPublished - 2016


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