Diffeology

Description:

"Diffeology is an extension of differential geometry. With a minimal set of axioms, diffeology allows us to deal simply but rigorously with objects which do not fall within the usual field of differential geometry: quotients of manifolds (even non-Hausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard set-theoretic operations, such as quotients, products, coproducts, subsets, limits, and colimits. With its right balance between rigor and simplicity, diffeology can be a good framework for many problems that appear in various areas of physics. Actually, the book lays the foundations of the main fields of differential geometry used in theoretical physics: differentiability, Cartan differential calculus, homology and cohomology, diffeological groups, fiber bundles, and connections. The book ends with an open program on symplectic diffeology, a rich field of application of the theory. Many exercises with solutions make this book appropriate for learning the subject."--Publisher's website.

subjects: Algebraic topology -- Fiber spaces and bundles -- Fiber spaces and bundles,  Differential geometry -- Global differential geometry -- Global differential geometry,  Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential spaces,  Differential geometry -- Symplectic geometry, contact geometry -- Symplectic geometry, contact geometry,  Algebraic topology -- Homotopy theory -- Loop spaces,  Differentiable manifolds,  Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms,  Algebraic topology -- Fiber spaces and bundles -- Generalizations of fiber spaces and bundles,  Symplectic geometry,  Algebraic topology -- Homotopy theory -- Homotopy theory,  Global differential geometry,  Global analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Infinite-dimensional manifolds,  Algebraic topology,  Geometry, differential,  Global analysis (mathematics),  Differential geometry,  Symplectic geometry, contact geometry,  Homotopy theory,  Loop spaces,  Fiber spaces and bundles,  Generalizations of fiber spaces and bundles,  Global analysis, analysis on manifolds,  General theory of differentiable manifolds,  Differential forms,  Differential spaces,  Infinite-dimensional manifolds,  Globale Differentialgeometrie,  Symplektische Geometrie,  Algebraische Topologie,  Differenzierbare Mannigfaltigkeit