An introduction to manifolds
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 int...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre numérique |
| Lenguaje: | Anglais |
| Publicado: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2008. |
| Colección: | Universitext
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| Materias: | |
| Acceso en línea: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 350 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • An introduction to manifolds, Loring W. Tu, 2008, New York, Springer, 1 vol. (XV-360 p.), Universitext, 978-0-387-48098-5 • Agency theory, information, and incentives, Günter Bamberg and Klaus Spremann (eds.), Berlin, Springer-Verlag, 1989, 1 vol. (XVIII-533 p.), 0-387-51675-1 |
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| 041 | 0 | |a eng | |
| 082 | |a 514.34 | ||
| 084 | |a 58-01. 2010 | ||
| 084 | |a 58Axx. 2010 | ||
| 084 | |a 58A05. 2010 | ||
| 100 | 1 | |a Tu, Loring W., |d 1952-...., |c mathématicien. | |
| 245 | 1 | 0 | |a An introduction to manifolds |c Loring W. Tu. |
| 250 | |a 1st ed. 2008. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Universitext |x 2191-6675 | |
| 500 | |a L'impression du document génère 350 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a 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. | |
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 650 | |a Cohomologie de de Rham | ||
| 650 | |a Formes différentielles | ||
| 650 | |a Lie, Algèbres de | ||
| 650 | |a Variétés (mathématiques) | ||
| 650 | |a Sous-variétés (mathématiques) | ||
| 650 | |a Lie, Groupes de | ||
| 776 | 0 | |0 12087184X |t An introduction to manifolds |f Loring W. Tu |d 2008 |c New York |n Springer |p 1 vol. (XV-360 p.) |s Universitext |z 978-0-387-48098-5 | |
| 776 | 0 | |0 021279160 |t Agency theory, information, and incentives |f Günter Bamberg and Klaus Spremann (eds.) |c Berlin |n Springer-Verlag |d 1989 |p 1 vol. (XVIII-533 p.) |z 0-387-51675-1 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-0-387-48101-2 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-SDFRSNLG-3 |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747872473 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-0-387-48101-2 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750884746 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-0-387-48101-2 |z Accès INSA CVL | |
| 997 | |0 940040 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||