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Diffeology
 
Patrick Iglesias-Zemmour CNRS, Marseille, France and The Hebrew University of Jerusalem, Jerusalem, Israel
Diffeology
Hardcover ISBN:  978-0-8218-9131-5
Product Code:  SURV/185
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-9452-1
Product Code:  SURV/185.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-9131-5
eBook: ISBN:  978-0-8218-9452-1
Product Code:  SURV/185.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Diffeology
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Diffeology
Patrick Iglesias-Zemmour CNRS, Marseille, France and The Hebrew University of Jerusalem, Jerusalem, Israel
Hardcover ISBN:  978-0-8218-9131-5
Product Code:  SURV/185
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-9452-1
Product Code:  SURV/185.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-9131-5
eBook ISBN:  978-0-8218-9452-1
Product Code:  SURV/185.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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.

Readership

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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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