The basics of differentiable manifolds, global calculus, differential geometry, and related topics constitute a core of information essential for the firstor second year graduate student preparing for advanced courses and seminars in differential topology and geometry. Differentiable Manifolds is a text designed to cover this material in a careful and sufficiently detailed manner, presupposing only a good foundation in general topology, calculus, and modern algebra. This second edition contains a significant amount of new material, which,in addition to classroom use, will make it a useful reference text. Topics that can be omitted safely in a first course are clearly marked, making this edition easier to use for such a course, as well as for private study by non-specialists wishing to survey the field. The themes of linearization, (re) integration, and global versus local calculus are emphasized throughout. One of the best introductions to differential manifolds available Includes extensive appendices and detailed diagrams INDICE: Preface to the Second Edition.- Topological Manifolds.- The Local Theory of Smooth Functions.- The Global Theory of Smooth Functions.- Flows andFoliations.- Lie Groups and Lie Algebras.- Covectors and 1--Forms.- Multilinear Algebra and Tensors.- Integration of Forms and de Rham Cohomology.- Forms and Foliations.- Riemannian Geometry.- Principal Bundles.- Appendix A. Construction of the Universal Covering.- Appendix B. Inverse Function Theorem.- Appendix C. Ordinary Differential Equations.- Appendix D. The de Rham Cohomology Theorem.- Bibliography.- Index.
- ISBN: 978-0-8176-4766-7
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 435
- Fecha Publicación: 01/02/2008
- Nº Volúmenes: 1
- Idioma: Inglés