Lectures on Symplectic Geometry
by Ana Cannas da Silva
Publisher: Springer 2006
Number of pages: 225
An introduction to symplectic geometry and topology, it provides a useful and effective synopsis of the basics of symplectic geometry and serves as the springboard for a prospective researcher. From an introductory chapter of symplectic forms and symplectic algebra, the book moves on to many of the subjects that serve as the basis for current research: symplectomorphisms, Lagrangian submanifolds, the Moser theorems, Darboux-Moser-Weinstein theory, almost complex structures, KAhler structures, Hamiltonian mechanics, symplectic reduction, etc.
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by Michael Muger - Radboud University
Contents: Why Differential Topology? Basics of Differentiable Manifolds; Local structure of smooth maps; Transversality Theory; More General Theory; Differential Forms and de Rham Theory; Tensors and some Riemannian Geometry; Morse Theory; etc.
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These notes describe basic material about smooth manifolds (vector fields, flows, tangent bundle, partitions of unity, Whitney embedding theorem, foliations, etc...), introduction to Morse theory, and various applications.
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Tight and taut submanifolds form an important class of manifolds with special curvature properties, one that has been studied intensively by differential geometers since the 1950's. This book contains six articles by leading experts in the field.
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The historical driving force of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. This text is occupied with the theory of differential forms and the exterior derivative.