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Diffeology

Author: Patrick Iglesias-Zemmour
Publisher: Providence, Rhode Island : American Mathematical Society, [2013]
Series: Mathematical surveys and monographs, no. 185.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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,  Read more...
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Details

Document Type: Book
All Authors / Contributors: Patrick Iglesias-Zemmour
ISBN: 9780821891315 0821891316
OCLC Number: 809925998
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.
Responsibility: Patrick Iglesias-Zemmour.

Abstract:

"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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