عنوان

Diffeology /

0821891316

9780821891315

b416414

Diffeology /

[Book]

Patrick Iglesias-Zemmour

xxiii, 439 pages ;

26 cm

Mathematical surveys and monographs ;

v. 185

Includes bibliographical references

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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"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

Algebraic topology

Differentiable manifolds

Global differential geometry

Symplectic geometry

Iglesias-Zemmour, Patrick,1953-

20150226102250.0

rda

[Book]

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