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An Introduction to Manifolds
Taschenbuch von Loring W. Tu
Sprache: Englisch

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Beschreibung
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. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
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. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Über den Autor
Loring W. Tu was born in Taipei, Taiwan, and grew up in Taiwan,Canada, and the United States. He attended McGill University and Princeton University as an undergraduate, and obtained his Ph.D. from Harvard University under the supervision of Phillip A. Griffiths. He has taught at the University of Michigan, Ann Arbor, and at Johns Hopkins University, and is currently Professor of Mathematics at Tufts University in Massachusetts. 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. He is the coauthor with Raoul Bott of "Differential Forms in Algebraic Topology."
Zusammenfassung

Many historical references have been added to the bibliography Hints and solutions are provided for selected exercises making this book ideal for self-study Further improves upon an already successful first edition Provides a comprehensive understanding of a large body of important mathematics in geometry and topology

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface to the Second Edition.- Preface to the First Edition.- 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.- Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xviii
410 S.
123 s/w Illustr.
1 farbige Illustr.
410 p. 124 illus.
1 illus. in color.
ISBN-13: 9781441973993
ISBN-10: 1441973990
Sprache: Englisch
Herstellernummer: 80017577
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Tu, Loring W.
Auflage: 2nd ed. 2011
Hersteller: Springer New York
Springer US, New York, N.Y.
Universitext
Maße: 235 x 155 x 24 mm
Von/Mit: Loring W. Tu
Erscheinungsdatum: 06.10.2010
Gewicht: 0,651 kg
Artikel-ID: 107464443
Über den Autor
Loring W. Tu was born in Taipei, Taiwan, and grew up in Taiwan,Canada, and the United States. He attended McGill University and Princeton University as an undergraduate, and obtained his Ph.D. from Harvard University under the supervision of Phillip A. Griffiths. He has taught at the University of Michigan, Ann Arbor, and at Johns Hopkins University, and is currently Professor of Mathematics at Tufts University in Massachusetts. 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. He is the coauthor with Raoul Bott of "Differential Forms in Algebraic Topology."
Zusammenfassung

Many historical references have been added to the bibliography Hints and solutions are provided for selected exercises making this book ideal for self-study Further improves upon an already successful first edition Provides a comprehensive understanding of a large body of important mathematics in geometry and topology

Includes supplementary material: [...]

Inhaltsverzeichnis
Preface to the Second Edition.- Preface to the First Edition.- 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.- Appendices.- A. Point-Set Topology.- B. The Inverse Function Theorem on R(N) and Related Results.- C. Existence of a Partition of Unity in General.- D. Linear Algebra.- E. Quaternions and the Symplectic Group.- Solutions to Selected Exercises.- Hints and Solutions to Selected End-of-Section Problems.- List of Symbols.- References.- Index.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xviii
410 S.
123 s/w Illustr.
1 farbige Illustr.
410 p. 124 illus.
1 illus. in color.
ISBN-13: 9781441973993
ISBN-10: 1441973990
Sprache: Englisch
Herstellernummer: 80017577
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Tu, Loring W.
Auflage: 2nd ed. 2011
Hersteller: Springer New York
Springer US, New York, N.Y.
Universitext
Maße: 235 x 155 x 24 mm
Von/Mit: Loring W. Tu
Erscheinungsdatum: 06.10.2010
Gewicht: 0,651 kg
Artikel-ID: 107464443
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