A general Fredholm theory III: Fredholm functors and polyfolds

By Helmut Hofer, K. Wysocki, E. Zehnder. 2008

77 citations recorded by the source corpus.

This is the third in a series of papers devoted to a general Fredholm theory in a new class of spaces, called polyfolds. We first introduce ep–groupoids and polyfolds. Then we generalize the Fredholm theory, which for M–polyfolds has been presented in our paper [22], to the more general polyfold setting. The Fredholm theory consists of a transversality and a perturbation theory. The results form the basis for our application to Symplectic Field Theory.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/06e272749bcad2a9f16013d59c83d704db36eeba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Frederick J. Bourgeois III
2. K. Wysocki
3. E. Zehnder
4. Helmut Hofer
5. Y. Eliashberg
6. T. Ekholm

In Geometry and Topology

1. T. Ekholm
2. Frederick J. Bourgeois III
3. Y. Eliashberg
4. Michael Hutchings
5. Helmut Hofer
6. K. Wysocki
7. E. Zehnder
8. A. Oancea

In Mathematical Physics

1. T. Ekholm
2. Frederick J. Bourgeois III
3. Y. Eliashberg
4. Helmut Hofer
5. K. Wysocki
6. E. Zehnder
7. A. Oancea
8. Michael Hutchings

Citations in the corpus

• Polyfold and Fredholm Theory (2014, background): “The initial version of the paper, [22], was written in 2008 on the occasion of a lecture given at the Clay Mathematical Institute (CMI), and described the theory as developed in [24, 25, 26].”
• Sc-Smoothness, Retractions and New Models for Smooth Spaces (2010, methodology): “We note that the notion of proper has to be reformulated for our generalization as is explained in [11].”
• Effect of Legendrian surgery (2009, methodology): “However for the purposes of this exposition we ignore this difficulty and claim that the correct version can be built according to the scheme presented here using one of the, for this purpose, currently developed technologies, notably, the polyfold theory of H Hofer, K Wysocki, and E Zehnder [31; 32”