DiffeologyPatrick Iglesias-ZemmouLabel: American Mathematical SocietyDescription: 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.
