2025/08/15 by Iglesias-Zemmour, Patrick
Computer Science · Mathematics · #53D20 #53D50 #55R10 #58A05 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 58A40 #Secondary 57S15 #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2508.11264
openalex publication_date 2025/08/15 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
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.