On regularities and Fredholm theory

Instantons on Conic 4-manifolds: Fredholm Theory

We study the self-duality operator on conic 4-manifolds. The self-duality operator can be identified as a regular singular operator in the sense of Brüning and Seeley, based on which we construct its parametrizations and closed extensions. We also compute the indexes.

A General Fredholm Theory III: Fredholm Functors and Polyfolds

2 Ep-Groupoids and Generalized Maps 17 2.1 Ep-Groupoids . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Functors and Equivalences . . . . . . . . . . . . . . . . . . . . 21 2.3 Inversion of Equivalences and Generalized Maps . . . . . . . . 28 2.4 Strong Bundles over Ep-Groupoids . . . . . . . . . . . . . . . 33 2.5 Auxiliary Norms . . . . . . . . . . . . . . . . . . . . . . . . . 4...

Introductory Fredholm theory and computation

We provide an introduction to Fredholm theory and discuss using the Fredholm determinant to compute pure-point spectra.

A General Fredholm Theory and Applications

The theory described here results from an attempt to find a general abstract framework in which various theories, like Gromov-Witten Theory (GW), Floer Theory (FT), Contact Homology (CH) and more generally Symplectic Field Theory (SFT) can be understood from a general point of view. Let us describe the general landscape in a somewhat oversimplified form. The common feature (with the exception o...

Polyfolds And A General Fredholm Theory