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" Diffeology / "
Patrick Iglesias-Zemmour
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BL
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| Record Number
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587195
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| Doc. No
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b416414
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| Main Entry
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Iglesias-Zemmour, Patrick,1953-
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| Title & Author
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Diffeology /\ Patrick Iglesias-Zemmour
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| Series Statement
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Mathematical surveys and monographs ;; v. 185
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| Page. NO
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xxiii, 439 pages ;; 26 cm
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| ISBN
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9780821891315
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: 0821891316
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| Bibliographies/Indexes
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Includes bibliographical references
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| Contents
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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
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| Abstract
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"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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| Subject
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Global differential geometry
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Symplectic geometry
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Algebraic topology
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Differentiable manifolds
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| Dewey Classification
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516.3/62
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| LC Classification
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QA670.I35 2013
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