nLab
polyfold

Hofer’s theory of polyfolds may be viewed a certain kind of generalized smooth spaces. The bulk of a theory developed by Helmut Hofer is a generalized approach to Fredholm operator analysis of geometrical origin, which gives a unified framework for symplectic field theory, Floer homology, some constructions in contact geometry etc.

References

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, Polyfolds and a general Fredholm theory, arXiv/0809.3753

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, Integration theory for zero sets of polyfold Fredholm sections, arXiv/0711.0781

• Helmut Hofer, Kris Wysocki, Eduard Zehnder, A general Fredholm theory I: A splicing-based differential geometry, arXiv/0612604; A general Fredholm theory II: implicit function theorems, arXiv/0705.1310; A general Fredholm theory III: Fredholm functors and polyfolds, arXiv

• Helmut H. Hofer, A general Fredholm theory and applications, arXiv/math/0509366

We thank Eugene Lerman for some of the information here.