nLab
polyfold

Eugene Lerman kindly provided the following information on Hofer’s theory of polyfolds, apparently a certain kind of generalized smooth spaces.

Reviews

• Katrin Werheim’s quick introduction.

• Hofer’s lectures at Stanford on polyfolds (a more complete version is here but for the time being (?) it’s password protected).

Articles by Hofer and his collaborators in the arxiv

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, A General Fredholm Theory III: Fredholm Functors and Polyfolds, arXiv.

• Helmut Hofer, Polyfolds And A General Fredholm Theory, arXiv.

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, Integration Theory for Zero Sets of Polyfold Fredholm Sections, arXiv.

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, A General Fredholm Theory II: Implicit Function Theorems, arXiv.

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, A General Fredholm Theory I: A Splicing-Based Differential Geometry, arXiv.

• Helmut H. Hofer, A General Fredholm Theory and Applications, arXiv.