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.
Home page url
Download or read it online for free here:
by Nigel Hitchin
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.
by Uwe Kaiser - Boise State University
This is a preliminary version of introductory lecture notes for Differential Topology. We try to give a deeper account of basic ideas of differential topology than usual in introductory texts. Many examples of manifolds are worked out in detail.
by Karl-Hermann Neeb - FAU Erlangen-Nuernberg
From the table of contents: Basic Concepts (The concept of a fiber bundle, Coverings, Morphisms...); Bundles and Cocycles; Cohomology of Lie Algebras; Smooth G-valued Functions; Connections on Principal Bundles; Curvature; Perspectives.
by Thomas E. Cecil, Shiing-shen Chern - Cambridge University Press
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.