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Lectures on the Geometry of Manifolds - Nicolaescu, Liviu I.
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Nicolaescu, Liviu I.:

Lectures on the Geometry of Manifolds - neues Buch

2013, ISBN: 9789810228361

ID: 1214777

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: Poincaré 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 Hölder 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, Weizenböck formulæ Mathematics Mathematics eBook, World Scientific Publishing Company

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Lectures on the Geometry of Manifolds - Nicolaescu, Liviu I.
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
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Nicolaescu, Liviu I.:

Lectures on the Geometry of Manifolds - neues Buch

2013, ISBN: 9789810228361

ID: 1214777

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: Poincaré 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 Hölder 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, Weizenböck formulæ Mathematics Mathematics, World Scientific Publishing Company

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Lecture Notes on the Geometry of Manifolds - Liviu I. Nicolaescu
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Liviu I. Nicolaescu:
Lecture Notes on the Geometry of Manifolds - gebunden oder broschiert

ISBN: 9810228368

[SR: 6233553], Hardcover, [EAN: 9789810228361], World Scientific Publishing Co Pte Ltd, World Scientific Publishing Co Pte Ltd, Book, [PU: World Scientific Publishing Co Pte Ltd], World Scientific Publishing Co Pte Ltd, 278353, Geometry & Topology, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 922942, Maths, 922518, Chaos, 922944, Recreational, 922868, Popular Science, 57, Science & Nature, 1025612, Subjects, 266239, Books, 570936, Geometry, 564352, Mathematics, 564334, Scientific, Technical & Medical, 1025612, Subjects, 266239, Books

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LECTURES ON THE GEOMETRY OF MANIFOLDS - NICOLAESCU LIVIU
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NICOLAESCU LIVIU:
LECTURES ON THE GEOMETRY OF MANIFOLDS - Taschenbuch

1996, ISBN: 9789810228361

ID: 688428905

WORLD SCIENTIFIC, 1996. Softcover. New. Orders usually ship within 1-2 business days. For expedite orders, we use FEDEX/UPS/DHL and receive fast within 3-5 business days with tracking number, no shipping to PO BOX, APO, FPO addresses. Kindly provide phone number for expedite delivery. 100% Customer satisfaction guaranteed!, WORLD SCIENTIFIC, 1996

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Lectures on the Geometry of Manifolds - Nicolaescu, Liviu I.
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Lectures on the Geometry of Manifolds - gebunden oder broschiert

1996, ISBN: 9810228368

ID: 5269588568

[EAN: 9789810228361], Fine, [PU: Hackensack, New Jersey, U.S.A.: World Scientific Pub Co Inc], MANIFOLDS MATHEMATICS GEOMETRY DIFFERENTIAL, Mathematics|Geometry|Differential, Jacket, hardback book and dust jacket in fine condition

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Details zum Buch
Lectures on the Geometry of Manifolds
Autor:

Nicolaescu, Liviu I.

Titel:

Lectures on the Geometry of Manifolds

ISBN-Nummer:

9810228368

It mainly deals with global questions and in particular the interdependence of geometry and topology, global and local. Algebraico-topological techniques are developed in the special context of smooth manifolds. The book discusses the DeRham cohomology and its ramifications: Poincare, duality, intersection theory, degree theory, Thom isomorphism, characteristic classes, Gauss-Bonnet etc. The authors seek to calculate the cohomology groups of as many as possible concrete examples without relying on the apparatus of homotopy theory (CW-complexes etc). Elliptic partial differential equations are also featured, requiring a familiarity with functional analysis. It describes the proofs of elliptic Lp and Holder estimates (assuming some deep results of harmonic analysis) for arbitrary elliptic operators with smooth coefficients. The book closes with alook at a class of elliptic operators, the Dirac operators. It discusses their algebraic structure in some detail, Weizenbock formulae and many concrete examples.

Detailangaben zum Buch - Lectures on the Geometry of Manifolds


EAN (ISBN-13): 9789810228361
ISBN (ISBN-10): 9810228368
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1996
Herausgeber: WORLD SCIENTIFIC PUB CO (
480 Seiten
Gewicht: 0,821 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 29.05.2007 15:57:22
Buch zuletzt gefunden am 30.07.2016 16:26:40
ISBN/EAN: 9810228368

ISBN - alternative Schreibweisen:
981-02-2836-8, 978-981-02-2836-1

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