Introduction to smooth manifolds
This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and em...
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Édition: | 2nd ed. 2012. |
| Collection: | Graduate Texts in Mathematics
218 |
| Sujets: | |
| Accès en ligne: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Note: |
Titre provenant de l'écran-titre Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to smooth manifolds, John M. Lee, 2nd edition, 2013, New York, Springer, 1 vol. (XV-708 p.), Graduate texts in mathematics, 978-1-4419-9981-8 • Introduction to Smooth Manifolds, Texte imprimé, 9781441999832 |
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| 100 | 1 | |a Lee, John M., |d 1950-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Introduction to smooth manifolds |c John M. Lee. |
| 250 | |a 2nd ed. 2012. | ||
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 218 |x 2197-5612 | |
| 500 | |a Titre provenant de l'écran-titre | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Preface 1 Smooth Manifolds 2 Smooth Maps 3 Tangent Vectors 4 Submersions, Immersions, and Embeddings 5 Submanifolds 6 Sard's Theorem 7 Lie Groups 8 Vector Fields 9 Integral Curves and Flows 10 Vector Bundles 11 The Cotangent Bundle 12 Tensors 13 Riemannian Metrics 14 Differential Forms 15 Orientations 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.- 22 Symplectic Manifolds Appendix A: Review of Topology Appendix B: Review of Linear Algebra Appendix C: Review of Calculus Appendix D: Review of Differential Equations References Notation Index Subject Index | |
| 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 This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis | ||
| 650 | |a Variétés (mathématiques) | ||
| 650 | |a Géométrie différentielle | ||
| 776 | 0 | |0 164447229 |t Introduction to smooth manifolds |f John M. Lee |e 2nd edition |d 2013 |c New York |n Springer |p 1 vol. (XV-708 p.) |s Graduate texts in mathematics |z 978-1-4419-9981-8 | |
| 776 | 0 | |t Introduction to Smooth Manifolds |b Texte imprimé |z 9781441999832 | |
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