Why Diffeology?

TL;DR

This paper introduces diffeology as a framework that generalizes differential geometry to complex spaces like singular and infinite-dimensional spaces, demonstrating its usefulness in various mathematical contexts.

Contribution

It highlights the key features of diffeology and illustrates its applications in singular spaces, symplectic geometry, and prequantization, expanding the scope of differential geometry.

Findings

Diffeology effectively handles singular and quotient spaces.

It provides a natural framework for infinite-dimensional geometry.

Applications include symplectic geometry and prequantization.

Abstract

Diffeology extends differential geometry to spaces beyond smooth manifolds. This paper explores diffeology's key features and illustrates its utility with examples including singular and quotient spaces, and applications in symplectic geometry and prequantization. Diffeology provides a natural and effective framework for handling complexities from singularities and infinite-dimensional settings.