An Introduction to Manifolds / Tu, Loring W (2008)  

Público ISBD Título : An Introduction to Manifolds Tipo de documento: documento electrónico Autores: Tu, Loring W ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVI, 368 p. 104 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-48101-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Complex  manifolds  and  Cell  Complexes  (incl.  Diff.Topology)  Analysis  on  Geometry Clasificación: 51 Matemáticas Resumen: 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, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology. Nota de contenido: Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance En línea: http://dx.doi.org/10.1007/978-0-387-48101-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34148 An Introduction to Manifolds [documento electrónico] / Tu, Loring W ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XVI, 368 p. 104 illus : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-0-387-48101-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Complex  manifolds  and  Cell  Complexes  (incl.  Diff.Topology)  Analysis  on  Geometry Clasificación: 51 Matemáticas Resumen: 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, An Introduction to Manifolds is also an excellent foundation for Springer GTM 82, Differential Forms in Algebraic Topology. Nota de contenido: Euclidean Spaces -- Smooth Functions on a Euclidean Space -- Tangent Vectors in Rn as Derivations -- Alternating k-Linear Functions -- Differential Forms on Rn -- Manifolds -- Manifolds -- Smooth Maps on a Manifold -- Quotients -- Lie Groups and Lie Algebras -- The Tangent Space -- Submanifolds -- Categories and Functors -- The Rank of a Smooth Map -- The Tangent Bundle -- Bump Functions and Partitions of Unity -- Vector Fields -- Lie Groups and Lie Algebras -- Lie Groups -- Lie Algebras -- Differential Forms -- Differential 1-Forms -- Differential k-Forms -- The Exterior Derivative -- Integration -- Orientations -- Manifolds with Boundary -- Integration on a Manifold -- De Rham Theory -- De Rham Cohomology -- The Long Exact Sequence in Cohomology -- The Mayer–Vietoris Sequence -- Homotopy Invariance -- Computation of de Rham Cohomology -- Proof of Homotopy Invariance En línea: http://dx.doi.org/10.1007/978-0-387-48101-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34148

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An Introduction to Manifolds / Tu, Loring W (2011)  

Público ISBD Título : An Introduction to Manifolds Tipo de documento: documento electrónico Autores: Tu, Loring W ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 410 p. 124 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-7400-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Complex  manifolds  and  Cell  Complexes  (incl.  Diff.Topology)  Analysis  on  Geometry Clasificación: 51 Matemáticas Resumen: 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. 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 second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: 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 En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161 An Introduction to Manifolds [documento electrónico] / Tu, Loring W ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVIII, 410 p. 124 illus., 1 illus. in color : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4419-7400-6 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Complex  manifolds  and  Cell  Complexes  (incl.  Diff.Topology)  Analysis  on  Geometry Clasificación: 51 Matemáticas Resumen: 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. 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 second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: 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 En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161

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