by Nigel Hitchin
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 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 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.
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.
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.