Diffeology (PDF)
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...
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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.
Bibliographische Angaben
- Autor: Patrick Iglesias-Zemmour
- 2013, 439 Seiten
- ISBN-10: 0821894528
- ISBN-13: 9780821894521
- Erscheinungsdatum: 04.09.2013
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
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