The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. From the standpoint of non-experts needing to learn some differential geometry for use in other parts of mathematics the choice of text is often a bit of a problem. To be sure, these fine books, and many others besides, are aimed at graduate students and have made their mark in no uncertain terms. But it cannot be denied that the plethora of connections between differential geometry, or the theory of differentiable manifolds, and other parts of mathematics algebraic topology, Lie groups, Riemannian geometry, etc. On top of this the whole business is complicated complexified?
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An Introduction to Manifolds. Loring W. Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.
In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology.
Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study.
Chapter 1 Euclidean Spaces. Chapter 2 Manifolds. Chapter 3 The Tangent Space. Chapter 4 Lie Groups and Lie Algebras. Chapter 5 Differential Forms. Chapter 6 Integration. Chapter 7 De Rham Theory. Solutions to Selected ExercisesWithin the Text. List of Notations. An Introduction to Manifolds Loring W.
An algebraic geometer by training, he has done research at the interface of algebraic geometry,topology, and differential geometry, including Hodge theory, degeneracy loci, moduli spaces of vector bundles, and equivariant cohomology. A Brief Introduction.
An Introduction to Manifolds
It seems that you're in Germany. We have a dedicated site for Germany. Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory.