higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
The notion of polyfolds, due to Helmut Hofer, is a notion of generalized smooth spaces. The bulk of the theory is a generalized approach to Fredholm operator analysis in geometrical situations; which can be considered as an analytic framework designed to systematically resolve the issue of transversality. It gives a unified framework for symplectic field theory, Floer homology, and some constructions in contact geometry etc.
Joel W. Fish, Helmut Hofer, Lectures on Polyfolds and Symplectic Field Theory (arXiv:1808.07147)
Helmut Hofer, A general Fredholm theory and applications (arXiv:math/0509366)
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:0810.0736)
Helmut Hofer, Kris Wysocki, Eduard Zehnder, Integration theory for zero sets of polyfold Fredholm sections (arXiv/0711.0781)
Helmut Hofer, Polyfolds and a general Fredholm theory (arXiv/0809.3753)
Helmut Hofer, Polyfolds and Fredholm Theory, Oxford University Press (2017) (doi:10.1093/oso/9780198784913.003.0004)
We thank Eugene Lerman for some of the information here.
Last revised on April 7, 2021 at 05:20:19. See the history of this page for a list of all contributions to it.