Introduction to Differential Topology
by Uwe Kaiser
Publisher: Boise State University 2006
Number of pages: 110
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. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail.
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by Ana Cannas da Silva
The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.
by John Morgan, Gang Tian - American Mathematical Society
This book provides full details of a complete proof of the Poincare Conjecture following Grigory Perelman's preprints. The book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.
by Ana Cannas da Silva - Princeton University
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.
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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.