Diffeology
By: Patrick Iglesias-Zemmour
Series: Mathematical surveys and monographs -- Volume 185
Publisher: American Mathematical Society
Published: 2013
Place of publication: Providence, Rhode Island
Language: eng
Number of pages: 439
ISBN-13: 9780821891315
Subjects: Algebraic topology -- Fiber spaces and bundles -- Fiber spaces and bundles; Differential geometry -- Global differential geometry -- Global differential geometry; Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential spaces; Differential geometry -- Symplectic geometry, contact geometry -- Symplectic geometry, contact geometry; Algebraic topology -- Homotopy theory -- Loop spaces; Differentiable manifolds; Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms; Algebraic topology -- Fiber spaces and bundles -- Generalizations of fiber spaces and bundles; Symplectic geometry; Algebraic topology -- Homotopy theory -- Homotopy theory; Global differential geometry; Global analysis, analysis on manifolds -- Infinite-dimensional manifolds -- Infinite-dimensional manifolds; Algebraic topology
Description: "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."--Publisher's website.
Notes: Includes bibliographical references.