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Introduction to Smooth Manifolds
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Bibliographic Detail
Publisher Springer Verlag
Publication date August 24, 2012
Pages 708
Binding Hardcover
Edition 2
Book category Adult Non-Fiction
ISBN-13 9781441999818
ISBN-10 1441999817
Dimensions 1.75 by 6.25 by 9 in.
Weight 2.55 lbs.
Original list price $99.00
Summaries and Reviews
Amazon.com description: Product Description:

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 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 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.



Editions
Hardcover
Book cover for 9780387954950 Book cover for 9781441999818
 
The price comparison is for this edition
2 edition from Springer Verlag (August 24, 2012)
9781441999818 | details & prices | 708 pages | 6.25 × 9.00 × 1.75 in. | 2.55 lbs | List price $99.00
About: This book is an introductory graduate-level textbook on the theory of smooth manifolds.
from Springer Verlag (November 1, 2002)
9780387954950 | details & prices | 628 pages | 6.50 × 9.50 × 1.25 in. | 2.25 lbs | List price $79.95
About: Author has written several excellent Springer books.
Paperback
Book cover for 9780387954486
 
from Springer Verlag (October 1, 2002)
9780387954486 | details & prices | 628 pages | 6.00 × 9.50 × 1.25 in. | 2.10 lbs | List price $64.95
About: Author has written several excellent Springer books.

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