Polyfolds and Fredholm Theory

TL;DR

This paper develops a new nonlinear Fredholm theory for specialized ambient spaces and categories, with an application to stable maps, advancing the mathematical framework for analyzing complex geometric structures.

Contribution

Introduces a novel Fredholm theory tailored for new ambient spaces and categories, expanding the tools available for geometric analysis.

Findings

Established a Fredholm framework for the new class of ambient spaces.

Applied the theory to the category of stable maps, demonstrating its utility.

Provided foundational results for future research in geometric analysis.

Abstract

We describe a (nonlinear) Fredholm theory for a new class of ambient spaces, as well as for a certain type of categories. The theory is illustrated by an application to the category of stable maps.