Introduction to Smooth Manifolds
Product ID: 75992418
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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 collectors, 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. . Review: Best introduction to smooth manifold - Modern THE book introducing smooth manifold theory that every graduate student must read. At a level suitable for graduate student, but covers huge amount of material which might take more than a year to go through. Review: Poor Binding - The book started coming apart at the seams of the binding and pages became loose. It was pathetic.
| Best Sellers Rank | #184,315 in Books ( See Top 100 in Books ) #80 in Geometry #782 in Library & Information Science |
| Customer Reviews | 4.6 out of 5 stars 154 Reviews |
C**1
Best introduction to smooth manifold
Modern THE book introducing smooth manifold theory that every graduate student must read. At a level suitable for graduate student, but covers huge amount of material which might take more than a year to go through.
D**M
Poor Binding
The book started coming apart at the seams of the binding and pages became loose. It was pathetic.
D**E
The Best on differentiable manifolds.
Best book to learn differential manifolds at introductory level. Prefer recent edition of this book.
R**A
Excelente produto
Apesar de ter tido problemas com a entrega, estou completamente satisfeito com o livro. Boa impressão e o livro veio intacto. As obras do John Lee são fundamentais para qualquer um com interesse em Variedades, principalmente para geômetras. Excelente referência! Este livro em específico traz variados tópicos além dos conteúdos fundamentais de Variedades Diferenciáveis, como Grupos de Lie e Cohomologia de de Rham.
Z**S
A very good book, but....
If you're interested in the subject then this is a very good book to have in your bag. It's detailed, comprehensive, and we'll organised - at least for my purposes in studying physics. But I do not find the subject beautiful, and the book didn't convince me otherwise. So a good book, but not one I'll hold close to my heart as a treasure. Note added: It has become my go-to book for the subject, which marks it as a must-have. The author has put a lot of work into providing a very comprehensive work, and one that is suitable for self-study.
A**Z
Perfect
The quality of paper, bending, cover, etc. are just perfect to me. I have not any complains about it. The contents are just amazing. I'm using it as one of the main references for my thesis and I recommend it to anyone who is learning about smooth manifolds. The proofs are clear and detailed, it has tons of examples and exercises, and also is self-contained. It has all the backround you need to fill in the Appendices section. It is a "graduate text" only because it has some advanced prerequisites, but once you have them, the book feels pretty readable and gentle.
V**L
Qualité top, emballage top, délais retardé mais sans exagération
Le livre était neuf de chez neuf et c'était bien la dernière édition. En effet, ce point est très important pour les connaisseurs. Les anciennes versions sont revendues parfois aux prix plein alors que la dernière est meilleure et plus complète.
D**N
Lee's books on smooth and Riemannian manifolds
are the best I have in my mathematics library. I frequently use them as reference, just recently to prepare my exam in GRT.
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