Volume: 185; 2013; 439 pp; Hardcover
MSC: Primary 53; 55; 58;
Print ISBN: 978-0-8218-9131-5
Product Code: SURV/185
List Price: $125.00
AMS Member Price: $100.00
MAA Member Price: $112.50
Electronic ISBN: 978-0-8218-9452-1
Product Code: SURV/185.E
List Price: $117.00
AMS Member Price: $93.60
MAA Member Price: $105.30
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Supplemental Materials
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.
Readership
Graduate students and research mathematicians interested in differential geometry and mathematical physics.
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