Polyfold mini-course (9 lectures)

Wehrheim/Fish/Hofer (9 lectures): Polyfolds and the construction of Symplectic Field Theory. Polyfold theory provides a language and a large body of results in an area, which is a mixture of a generalized differential geometry, nonlinear functional analysis, and category theory. It includes a very general concept of a Fredholm section accompanied by Sard-Smale type transversality theory over the rational numbers, i.e. perturbing through rationally weighted multi-sections. As such, it is a powerful tool to address complicated transversality issues as they arise in constructing compact moduli spaces in symplectic geometry. In the first week, Fish and Wehrheim will introduce the analytic foundations of polyfold theory, including the notions of sc-calculus, retracts, M-polyfolds, strong bundles, Fredholm sections and regularization theorems. In the second week, Hofer will build on these foundations, aiming to construct the moduli spaces needed for general Symplectic Field Theory.

Homework Problems

Reference material