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|All Authors / Contributors:||
|Description:||xxiii, 439 pages ; 26 cm.|
|Contents:||Chapter 1. Diffeology and Diffeological Spaces --
Chapter 2. Locality and Diffeologies --
Chapter 3. Diffeological Vector Spaces --
Chapter 4. Modeling Spaces, Manifolds, etc. --
Chapter 5. Homotopy of Diffeological Spaces --
Chapter 6. Cartan-De Rham Calculus --
Chapter 7. Diffeological Groups --
Chapter 8. Diffeological Fiber Bundles Chapter 9. Symplectic Diffeology.
|Series Title:||Mathematical surveys and monographs, no. 185.|
"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.
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- Global differential geometry.
- Symplectic geometry.
- Algebraic topology.
- Differentiable manifolds.
- Differential geometry -- Global differential geometry -- Global differential geometry.
- Differential geometry -- Symplectic geometry, contact geometry -- Symplectic geometry, contact geometry.
- Algebraic topology -- Homotopy theory -- Homotopy theory.
- Algebraic topology -- Homotopy theory -- Loop spaces.
- Algebraic topology -- Fiber spaces and bundles -- Fiber spaces and bundles.
- Algebraic topology -- Fiber spaces and bundles -- Generalizations of fiber spaces and bundles.
- Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms.
- Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential spaces.
- Global analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Infinite-dimensional manifolds.
- Globale Differentialgeometrie.
- Symplektische Geometrie.
- Algebraische Topologie.
- Differenzierbare Mannigfaltigkeit.