Transversality problems in symplectic field theory and a new Fredholm theory.

link: http://arxiv.org/abs/1003.0651
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.