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Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology,

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham the

An infinite-dimensional manifold is a topological manifold modeled on some infinite-dimensional homogeneous space called a model space. In this book, the follow

If X is a manifold then the R-algebra C∞(X) of smooth functions c:X→R is a C∞-ring. That is, for each smooth function f:Rn→R there is an n-fold operatio