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 in geometrical situations; it can be also considered as an “analytic framework designed to resolve the issue of transversality systematically”. It gives a unified framework for symplectic field theory, Floer homology, some constructions in contact geometry etc.



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.

Last revised on July 10, 2015 at 09:38:00. See the history of this page for a list of all contributions to it.