by Nigel Hitchin
Number of pages: 94
This is an introductory course on differentiable manifolds. One of the historical driving forces of the theory of manifolds was General Relativity, where the manifold is four-dimensional spacetime, wormholes and all. A large part of the text is occupied with the theory of differential forms and the exterior derivative.
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by Jie Wu - National University of Singapore
Contents: Tangent Spaces, Vector Fields in Rn and the Inverse Mapping Theorem; Topological and Differentiable Manifolds, Diffeomorphisms, Immersions, Submersions and Submanifolds; Examples of Manifolds; Fibre Bundles and Vector Bundles; etc.
by Hansjoerg Geiges - arXiv
This is an introductory text on the more topological aspects of contact geometry. After discussing some of the fundamental results of contact topology, I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem.
by Ana Cannas da Silva - Springer
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. The text is written in a clear, easy-to-follow style.
by George Torres, Robert Gompf - University of Texas at Austin
This is a course on contact manifolds, which are odd dimensional manifolds with an extra structure called a contact structure. Most of our study will focus on three dimensional manifolds, though many of these notions hold for any odd dimension.