Foundations of differentiable manifolds and Lie groups / Franck W. WarnerType de document : MonographieCollection : Graduate texts in mathematics, 94Langue : anglais.Pays: Etats Unis.Éditeur : New York : Springer-Verlag, 1983Description : 1 vol. (ix-272 p.) : ill. ; 25 cmISBN: 0387908943.ISSN: 0072-5285.Bibliographie : Bibliogr. p. 260-263. Index.Sujet MSC : 58-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to global analysis
22Exx, Topological groups, Lie groups - Lie groups
58Axx, Global analysis, analysis on manifolds - General theory of differentiable manifolds
58C35, Global analysis, analysis on manifolds, Integration on manifolds; measures on manifolds
53C30, Global differential geometry, Differential geometry of homogeneous manifoldsEn-ligne : Springerlink | Zentralblatt | MathSciNet Item type: Monographie
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Chapter 1, Manifolds; 2, Tensors and differential forms; 3, Lie Groups; 4, Integration on manifolds; 5, Sheaves, cohomology, and the de Rham theorem; 6, The Hodge theorem. These last two chapters assure this book a unique and extremely useful place among the "introductory books on manifold theory''.
Overall, the style is clear, clean, and formal, perhaps a bit thin on motivation, as is customary, except through examples and problems. The problems appearing after each chapter are elementary in the beginning, but after Chapter 2 the problems also contain significant major theorems. For example, the fundamental theorem on abelian Lie groups and the Peter-Weyl theorem are problems. Many problems are devoted to filling in necessary pieces of the text, e.g., a problem on the use of a partition of unity to prove the existence of a Riemannian metric is placed after Chapter 1, and problems on the star operator and the adjoint of left multiplication by a 1-form, both used in the Hodge theorem, are found after Chapter 2. (MathSciNet)
Bibliogr. p. 260-263. Index
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