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|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA613 | QA613. FCT 95775 (Browse shelf) | 1 | Available |
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| QA612.7.SPR FCT 82535 Stein manifolds and holomorphic mappings | QA612.7.SPR FCT 82773 Stable homotopy around the Arf-Kervaire invariant | QA613 | QA316.SPR FCT 82109 Variational inequalities and frictional contact problems | QA613 | QA613. FCT 95775 An introduction to manifolds | QA613 | QA613. FCT 96142 Diffeomorphisms of elliptic 3-manifolds | QA613 | QA613. FCT 96189 The geometry of Minkowski spacetime | QA613 | QA613. FCT 96210 Differentiable manifolds |
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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. .
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