Why Diffeology?

Published 15 Aug 2025 in math.DG | (2508.11264v1)

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.

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Patrick Iglesias-Zemmour

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