
Preface  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2013; 439 pp; hardcover Volume: 185 ISBN10: 0821891316 ISBN13: 9780821891315 List Price: US$117 Member Price: US$93.60 Order Code: SURV/185 See also: Global Analysis: Differential Forms in Analysis, Geometry and Physics  Ilka Agricola and Thomas Friedrich Topics in Differential Geometry  Peter W Michor  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 nonHausdorff), spaces of functions, groups of diffeomorphisms, etc. The category of diffeology objects is stable under standard settheoretic 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. 


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