**Mathematical Surveys and Monographs**

Volume: 185;
2013;
439 pp;
Hardcover

MSC: Primary 53; 55; 58;

Print ISBN: 978-0-8218-9131-5

Product Code: SURV/185

List Price: $117.00

Individual Member Price: $93.60

**Electronic ISBN: 978-0-8218-9452-1
Product Code: SURV/185.E**

List Price: $117.00

Individual Member Price: $93.60

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#### Supplemental Materials

# Diffeology

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*Patrick Iglesias-Zemmour*

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.

#### Table of Contents

# Table of Contents

## Diffeology

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xvii18 free
- Diffeology and diffeological spaces 126 free
- Locality and diffeologies 5176
- Diffeological vector spaces 6590
- Modeling spaces, manifolds, etc. 77102
- Homotopy of diffeological spaces 101126
- Cartan-De Rham calculus 125150
- Diffeological groups 215240
- Diffeological fiber bundles 229254
- Symplectic diffeology 299324
- Solutions of exercises 355380
- Afterword 429454
- Notation and vocabulary 433458
- Bibliography 437462
- Back Cover Back Cover1466

#### Readership

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