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Differentiable Manifolds (Pure and applied mathematics)
Differentiable Manifolds (Pure and applied mathematics)
Date: 23 May 2011, 15:34

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The theory of differentiable manifolds and Lie groups is a basis of the study of differential geometry and differential topology, and the recent development in various branches of mathematics shows that this theory is one of the cornerstones of the edifice of modern mathematics.
The intention of this book is to provide an introduction to the theory of differential manifolds and Lie groups. The book is designed as an advanced undergraduate course or an introductory graduate course and assumes a knowledge of the elements of algebra (vector spaces, groups), point set topology, and some amount of basic analysis.
This book arose from courses given by the author at Osaka University for senior undergraduate students and is a translation of a text published in Japanese in 1965 by Shokabo, Tokyo.
The basic materials (vector spaces, topological spaces, functions of several variables) which are indispensable for the rigorous understanding of the book are gathered in Chapter I. Besides these materials we assume a knowledge of the elements of function theory of one complex variable for the understanding of few sections concerning the complex manifolds and the complex differential forms. However the reader who is not familiar with complex analysis may skip these sections.

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