Introduction to Smooth Manifolds

Author:   John M. Lee
Publisher:   Springer-Verlag New York Inc.
Volume:   v. 218
ISBN:  

9780387954486


Pages:   645
Publication Date:   23 September 2002
Format:   Paperback
Availability:   Out of print, replaced by POD   Availability explained
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Introduction to Smooth Manifolds


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Overview

This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called differential geometry, in this book the author has decided to avoid use of this term because it applies more specifically to the study of smooth manifolds endowed with some extra structure, such as a Riemannian metric, a symplectic structure, a Lie group structure, or a foliation, and of the properties that are invariant under maps that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth.

Full Product Details

Author:   John M. Lee
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Volume:   v. 218
Dimensions:   Width: 15.60cm , Height: 3.40cm , Length: 23.40cm
Weight:   0.900kg
ISBN:  

9780387954486


ISBN 10:   0387954481
Pages:   645
Publication Date:   23 September 2002
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Out of Print
Availability:   Out of print, replaced by POD   Availability explained
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Reviews

From the reviews: This book offers a concise, clear, and detailed introduction to analysis on manifolds and elementary differential geometry. ! Some of the prerequisites are reviewed in an appendix. For the ambitious reader, lots of exercises and problems are provided. (A. Cap, Monatshefte fur Mathematik, Vol. 145 (4), 2005) The title of this 600 pages book is self-explaining. And in fact the book could have been entitled 'A smooth introduction to manifolds'. ! Also the notations are light and as smooth as possible, which is nice. ! The comprehensive theoretical matter is illustrated with many figures, examples, exercises and problems. Some of these exercises are quite deep ! . (Pascal Lambrechts, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2004) It introduces and uses all of the standard tools of smooth manifold theory and offers the proofs of all its fundamental theorems. ! This is a clearly and carefully written book in the author's usual elegant style. The exposition is crisp and contains a lot of pictures and intuitive explanations of how one should think geometrically about some abstract concepts. It could profitably be used by beginning graduate students who want to undertake a deeper study of specialized applications of smooth manifold theory. (Mircea Craioveanu, Zentralblatt MATH, Vol. 1030, 2004) This text provides an elementary introduction to smooth manifolds which can be understood by junior undergraduates. ! There are 157 illustrations, which bring much visualisation, and the volume contains many examples and easy exercises, as well as almost 300 'problems' that are more demanding. The subject index contains more than 2700 items! ! The pedagogic mastery, the long-life experience with teaching, and the deep attention to students' demands make this book a real masterpiece that everyone should have in their library. (EMS Newsletter, June, 2003) Prof. Lee has written the definitive modern introduction to manifolds. ! The material is very well motivated. He writes in a rigorous yet discursive style, full of examples, digressions, important results, and some applications. ! The exercises appearing in the text and at the end of the chapters are an excellent mix ! . it would make an ideal text for a comprehensive graduate-level course in modern differential geometry, as well as an excellent reference book for the working (applied) mathematician. (Peter J. Oliver, SIAM Review, Vol. 46 (1), 2004)


From the reviews: This book offers a concise, clear, and detailed introduction to analysis on manifolds and elementary differential geometry. ... Some of the prerequisites are reviewed in an appendix. For the ambitious reader, lots of exercises and problems are provided. (A. Cap, Monatshefte fur Mathematik, Vol. 145 (4), 2005) The title of this 600 pages book is self-explaining. And in fact the book could have been entitled 'A smooth introduction to manifolds'. ... Also the notations are light and as smooth as possible, which is nice. ... The comprehensive theoretical matter is illustrated with many figures, examples, exercises and problems. Some of these exercises are quite deep ... . (Pascal Lambrechts, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2004) It introduces and uses all of the standard tools of smooth manifold theory and offers the proofs of all its fundamental theorems. ... This is a clearly and carefully written book in the author's usual elegant style. The exposition is crisp and contains a lot of pictures and intuitive explanations of how one should think geometrically about some abstract concepts. It could profitably be used by beginning graduate students who want to undertake a deeper study of specialized applications of smooth manifold theory. (Mircea Craioveanu, Zentralblatt MATH, Vol. 1030, 2004) This text provides an elementary introduction to smooth manifolds which can be understood by junior undergraduates. ... There are 157 illustrations, which bring much visualisation, and the volume contains many examples and easy exercises, as well as almost 300 'problems' that are more demanding. The subject index contains more than 2700 items! ... The pedagogic mastery, the long-life experience with teaching, and the deep attention to students' demands make this book a real masterpiece that everyone should have in their library. (EMS Newsletter, June, 2003) Prof. Lee has written the definitive modern introduction to manifolds. ... The material is very well motivated. He writes in a rigorous yet discursive style, full of examples, digressions, important results, and some applications. ... The exercises appearing in the text and at the end of the chapters are an excellent mix ... . it would make an ideal text for a comprehensive graduate-level course in modern differential geometry, as well as an excellent reference book for the working (applied) mathematician. (Peter J. Oliver, SIAM Review, Vol. 46 (1), 2004)


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