Diffeology /

Diffeology /

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Bibliographic Details
Author / Creator:	Iglesias-Zemmour, Patrick, 1953-
Imprint:	Providence, Rhode Island : American Mathematical Society, [2013]
Description:	xxiii, 439 pages ; 26 cm.
Language:	English
Series:	Mathematical surveys and monographs ; v. 185 Mathematical surveys and monographs ; no. 185.
Subject:	Global differential geometry. Symplectic geometry. Algebraic topology. Differentiable manifolds. Algebraic topology. Differentiable manifolds. Global differential geometry. Symplectic geometry.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/9144286

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ISBN:	9780821891315 (alk. paper) 0821891316 (alk. paper)
Notes:	Includes bibliographical references.
Summary:	"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.

Description
Summary:	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, co-products, subsets, limits, and co-limits. 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.
Physical Description:	xxiii, 439 pages ; 26 cm.
Bibliography:	Includes bibliographical references.
ISBN:	9780821891315 0821891316