Why Diffeology?
arXiv:2508.11264
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.
48 pages, 4 figures. This is a survey on Diffeology. Keywords: Diffeology, Singular Spaces, Quotient Spaces, Orbifolds, Symplectic Geometry, Moment Map, Geometric Quantization, Prequantum Groupoid, Diffeological Bundles, Klein Stratification, Noncommutative Geometry