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. 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. Patrick Iglesias-zemmour. Includes Bibliographical References. Content: 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. 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 "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."--Résumé de l'éditeur Diffeology is the first textbook on the subject. It is aimed to graduate students and researchers who work in differential geometry or in mathematical physics
