Title
Introduction to Smooth Manifolds (Graduate Texts in Mathematics, Vol. 218),New
Delivery time: 8-12 business days (International)
This book is an introductory graduatelevel 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 fewnew 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 firstorder 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.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Introduction to Smooth Manifolds'? A: The book focuses on the theory of smooth manifolds, aiming to familiarize students with essential tools for mathematical or scientific research, including smooth structures, tangent vectors, differential forms, and Lie groups.
- Q: Who is the author of this textbook? A: The author of 'Introduction to Smooth Manifolds' is John Lee.
- Q: What are the prerequisites for reading this book? A: Prerequisites include a solid understanding of general topology, fundamental groups, covering spaces, as well as basic undergraduate linear algebra and real analysis.
- Q: Is this book suitable for beginners? A: Yes, it is designed as an introductory graduate-level textbook, making it suitable for students new to the theory of smooth manifolds.
- Q: What edition of the book is available? A: The available edition is the second edition, published on August 26, 2012.
- Q: How many pages does the book contain? A: The book contains a total of 724 pages.
- Q: What is the binding type of this textbook? A: The textbook is available in hardcover binding.
- Q: Does the book include new topics compared to the first edition? A: Yes, the second edition includes new topics such as Sard’s theorem, transversality, and a more thorough study of first-order partial differential equations.
- Q: What is the book's item condition? A: The item condition is new.
- Q: Is there a focus on visual aids in this textbook? A: Yes, the book includes pictures and intuitive discussions to help readers understand abstract concepts geometrically.