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Diffeology

Patrick Iglesias-Zemmour CNRS, Marseille, France and The Hebrew University of Jerusalem, Jerusalem, Israel
Available Formats:
Hardcover ISBN: 978-0-8218-9131-5
Product Code: SURV/185
List Price: $125.00 MAA Member Price:$112.50
AMS Member Price: $100.00 Electronic ISBN: 978-0-8218-9452-1 Product Code: SURV/185.E List Price:$117.00
MAA Member Price: $105.30 AMS Member Price:$93.60
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List Price: $187.50 MAA Member Price:$168.75
AMS Member Price: $150.00 Click above image for expanded view Diffeology Patrick Iglesias-Zemmour CNRS, Marseille, France and The Hebrew University of Jerusalem, Jerusalem, Israel Available Formats:  Hardcover ISBN: 978-0-8218-9131-5 Product Code: SURV/185  List Price:$125.00 MAA Member Price: $112.50 AMS Member Price:$100.00
 Electronic ISBN: 978-0-8218-9452-1 Product Code: SURV/185.E
 List Price: $117.00 MAA Member Price:$105.30 AMS Member Price: $93.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$187.50 MAA Member Price: $168.75 AMS Member Price:$150.00
• Book Details

Mathematical Surveys and Monographs
Volume: 1852013; 439 pp
MSC: Primary 53; 55; 58;

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.

Graduate students and research mathematicians interested in differential geometry and mathematical physics.

• Chapters
• 1. Diffeology and diffeological spaces
• 2. Locality and diffeologies
• 3. Diffeological vector spaces
• 4. Modeling spaces, manifolds, etc.
• 5. Homotopy of diffeological spaces
• 6. Cartan-De Rham calculus
• 7. Diffeological groups
• 8. Diffeological fiber bundles
• 9. Symplectic diffeology

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1852013; 439 pp
MSC: Primary 53; 55; 58;

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.

Graduate students and research mathematicians interested in differential geometry and mathematical physics.

• Chapters
• 1. Diffeology and diffeological spaces
• 2. Locality and diffeologies
• 3. Diffeological vector spaces
• 4. Modeling spaces, manifolds, etc.
• 5. Homotopy of diffeological spaces
• 6. Cartan-De Rham calculus
• 7. Diffeological groups
• 8. Diffeological fiber bundles
• 9. Symplectic diffeology
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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