The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set topology.We tried to address several issues. 1. The Language; 2. The Problems; 3. The Methods; 4. The Answers.Historically, the problems came first, ...
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The object of this book is to introduce the reader to some of the most important techniques of modern global geometry. In writing it we had in mind the beginning graduate student willing to specialize in this very challenging field of mathematics. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set topology.We tried to address several issues. 1. The Language; 2. The Problems; 3. The Methods; 4. The Answers.Historically, the problems came first, then came the methods and the language while the answers came last. The space constraints forced us to change this order and we had to painfully restrict our selection of topics to be covered. This process always involves a loss of intuition and we tried to balance this by offering as many examples and pictures as often as possible. We test most of our results and techniques on two basic classes examples: surfaces (which can be easily visualized) and Lie groups (which can be elegantly algebraized). When possible we present several facets of the same issue.We believe that a good familiarity with the formalism of differential geometry is absolutely necessary in understanding and solving concrete problems and this is why we presented it in some detail. Every new concept is supported by concrete examples interesting not only from an academic point of view.Our interest is mainly in global questions and in particular the interdependencegeometry topology, local global.We had to develop many algebraico-topological techniques in the special context of smooth manifolds. We spent a big portion of this book discussing the DeRham cohomology and its ramifications: Poincar??? duality, intersection theory, degree theory, Thom isomorphism, characteristic classes, Gauss-Bonnet etc. We tried to calculate the cohomology groups of as many as possible concrete examples and we had to do this without relying on the powerful apparatus of homotopy theory (CW-complexes etc.). Some of the proofs are not the most direct ones but the means are sometimes more interesting than the ends. For example in computing the cohomology of complex grassmannians we returned to classical invariant theory and used some brilliant but unadvertised old ideas.In the last part of the book we discuss elliptic partial differential equations. This requires a familiarity with functional analysis. We painstakingly described the proofs of elliptic Lp and H???lder estimates (assuming some deep results of harmonic analysis) for arbitrary elliptic operators with smooth coefficients. It is not a "light meal" but the ideas are useful in a large number of instances. We present a few applications of these techniques (Hodge theory, uniformization theorem). We conclude with a close look to a very important class of elliptic operators namely the Dirac operators. We discuss their algebraic structure in some detail, Weizenb???ck formul??? and many concrete examples.
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Add this copy of Lectures on the Geometry of Manifolds to cart. $222.67, like new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2007 by World Scientific Publishing Company.
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Fine. Sewn binding. Cloth over boards. 608 p. Contains: Line drawings, black & white, Tables, black & white, Figures. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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Fine. Sewn binding. Cloth over boards. 608 p. Contains: Line drawings, black & white, Tables, black & white, Figures. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Lectures on the Geometry of Manifolds to cart. $102.58, like new condition, Sold by Burwood Books rated 4.0 out of 5 stars, ships from Wickham Market, SUFFOLK, UNITED KINGDOM, published 1999 by World Scientific Publishing Company.
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Reprint. Hardback. Dust Jacket. 8vo. Original publishers black cloth, lettered gilt at the spine. ISBN: 9810228368 Pages: 500 Fine in fine dust jacket.
Add this copy of Lectures on the Geometry of Manifolds to cart. $117.14, good condition, Sold by Anybook rated 5.0 out of 5 stars, ships from Lincoln, UNITED KINGDOM, published 1996 by World Scientific Publishing.
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This is an ex-library book and may have the usual library/used-book markings inside. This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item, 850grams, ISBN: 9810228368.
Add this copy of Lectures on the Geometry of Manifolds to cart. $136.22, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1996 by World Scientific Publishing Co.
