Transversality problems in symplectic field theory and a new Fredholm theory
Oliver Fabert
TL;DR
This paper introduces the transversality problem in symplectic field theory and discusses a new Fredholm approach, serving as a prelude to a comprehensive guide on polyfolds for resolving these issues.
Contribution
It highlights the application of the new Fredholm theory by Hofer, Wysocki, and Zehnder to symplectic field theory transversality problems, paving the way for polyfold methods.
Findings
Illustrates the transversality issues in symplectic field theory
Motivates the use of the new Fredholm theory for these problems
Prepares for a detailed guide on polyfolds
Abstract
This survey wants to give a short introduction to the transversality problem in symplectic field theory and motivate to approach it using the new Fredholm theory by Hofer, Wysocki and Zehnder. With this it should serve as a lead-in for the user's guide to polyfolds, which will appear soon and is the result of a working group organized by J. Fish, R. Golovko and the author at MSRI Berkeley in fall 2009.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry