by Ana Cannas da Silva
Publisher: Princeton University 2004
Number of pages: 109
This is an overview of symplectic geometry – the geometry of symplectic manifolds. From a language for classical mechanics in the XVIII century, symplectic geometry has matured since the 1960’s to a rich and central branch of differential geometry and topology. A current survey can thus only aspire to give a partial flavor on this exciting field.
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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 Peter W. Michor - Birkhauser
This book is devoted to the theory of manifolds of differentiable mappings and contains result which can be proved without the help of a hard implicit function theorem of nuclear function spaces. All the necessary background is developed in detail.
by Bjorn Ian Dundas - Johns Hopkins University
This is an elementary text book for the civil engineering students with no prior background in point-set topology. This is a rather terse mathematical text, but provided with an abundant supply of examples and exercises with hints.
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.