1Vrije Universiteit Amsterdam, Netherlands 2University of Massachusetts Boston, USA 3Université Libre de Bruxelles, Belgium 4University of California Berkeley, United States
EMS surveys in mathematical sciences, Tome 3 (2016) no. 2, pp. 131-208
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.
Oliver Fabert
1
;
Joel W. Fish
2
;
Roman Golovko
3
;
Katrin Wehrheim
4
1
Vrije Universiteit Amsterdam, Netherlands
2
University of Massachusetts Boston, USA
3
Université Libre de Bruxelles, Belgium
4
University of California Berkeley, United States
Oliver Fabert; Joel W. Fish; Roman Golovko; Katrin Wehrheim. Polyfolds: A first and second look. EMS surveys in mathematical sciences, Tome 3 (2016) no. 2, pp. 131-208. doi: 10.4171/emss/16
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