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Graduate Studies in Mathematics
2008; 494 pp; hardcover
List Price: US$81
Member Price: US$64.80
Order Code: GSM/93
This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry.
The layout of the material stresses naturality and functoriality from the beginning and is as coordinate-free as possible. Coordinate formulas are always derived as extra information. Some attractive unusual aspects of this book are as follows:
This book gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra.
Graduate students, research mathematicians and physicists interested in differential geometry, mechanics, and relativity.
"...remarkably effective. ... Michors book is a truly marvelous pick from which to learn a lot of beautiful, important, and current mathematics."
-- MAA Reviews
"Throughout the book the author stresses the development of short exact sequences and takes evident delight in the applications that ensue. For the reviewer, this is one of the most enjoyable qualities of the text. The text is a treasure, and will open up to the diligent and patient reader a vast panorama of modern differential geometry."
-- Mathematical Reviews
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