Polyfolds: A first and second look

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

Research output: Contribution to JournalArticleAcademicpeer-review

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.
Original languageEnglish
Article numberDOI: 10.4171/EMSS/16
Pages (from-to)131–208
Number of pages78
JournalEMS Surveys in Mathematical Sciences
Volume3
Issue number2
DOIs
Publication statusPublished - 2016

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Pseudoholomorphic Curves
Fredholm Theory
Transversality
Elliptic PDE
Morse Theory
Differential Geometry
Compactification
Moduli Space
Smoothness
Banach space
Theorem
Model
Context
Framework

Cite this

Fabert, O., Fish, J., Golovko, R., & Wehrheim, K. (2016). Polyfolds: A first and second look. EMS Surveys in Mathematical Sciences, 3(2), 131–208. [DOI: 10.4171/EMSS/16]. https://doi.org/10.4171/EMSS/16
Fabert, O. ; Fish, Joel ; Golovko, Roman ; Wehrheim, Katrin. / Polyfolds: A first and second look. In: EMS Surveys in Mathematical Sciences. 2016 ; Vol. 3, No. 2. pp. 131–208.
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Fabert, O, Fish, J, Golovko, R & Wehrheim, K 2016, 'Polyfolds: A first and second look' EMS Surveys in Mathematical Sciences, vol. 3, no. 2, DOI: 10.4171/EMSS/16, pp. 131–208. https://doi.org/10.4171/EMSS/16

Polyfolds: A first and second look. / Fabert, O.; Fish, Joel; Golovko, Roman; Wehrheim, Katrin.

In: EMS Surveys in Mathematical Sciences, Vol. 3, No. 2, DOI: 10.4171/EMSS/16, 2016, p. 131–208.

Research output: Contribution to JournalArticleAcademicpeer-review

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Fabert O, Fish J, Golovko R, Wehrheim K. Polyfolds: A first and second look. EMS Surveys in Mathematical Sciences. 2016;3(2):131–208. DOI: 10.4171/EMSS/16. https://doi.org/10.4171/EMSS/16