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133,00 ۥ Diffeology and diffeological spaces 26Free
• Locality and diffeologies76
• Diffeological vector spaces90
• Modeling spaces, manifolds, etc.102
• Homotopy of diffeological spaces126
• Cartan-De Rham calculus150
• Diffeological groups240
• Diffeological fiber bundles254
• Symplectic diffeology324
• Solutions of exercises380
• Afterword454
• Notation and vocabulary458
• Bibliography
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.
Author
Patrick Iglesias-Zemmour: CNRS, Marseille, France and The Hebrew University of Jerusalem, Jerusalem, Israel
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