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Differential Topology (AMS Chelsea Publishing) Hardcover – August 16, 2010

ISBN-13: 978-0821851937 ISBN-10: 0821851934 Edition: Reprint

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Differential Topology (AMS Chelsea Publishing) + Topology from the Differentiable Viewpoint + Algebraic Topology
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Product Details

  • Hardcover: 222 pages
  • Publisher: American Mathematical Society; Reprint edition (August 16, 2010)
  • Language: English
  • ISBN-10: 0821851934
  • ISBN-13: 978-0821851937
  • Product Dimensions: 7.2 x 10.2 inches
  • Shipping Weight: 1.3 pounds (View shipping rates and policies)
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #370,011 in Books (See Top 100 in Books)

Editorial Reviews

From the Publisher

This text fits any course with the word "Manifold" in the title. It is a graduate level book. --This text refers to an out of print or unavailable edition of this title.

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3.8 out of 5 stars
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32 of 34 people found the following review helpful By Malcolm on September 22, 2008
Format: Hardcover
There are few books really suitable for undergraduates who wish to get a feel for differential topology, and among them Guillemin and Pollack is probably the best. Assuming only multivariate calculus, linear algebra, and some point-set topology (with a typical analysis class covering everything in the first and third categories), G&P presents an intuitive introduction to smooth manifolds with many pictures and simple examples while avoiding much of the formalism. It is most similar to Milnor's Topology from the Differentiable Viewpoint, upon which it was based, but it has additional material, most notably on differential forms and integration.

Books on differential topology (a.k.a. smooth manifolds or differential manifolds) tend to divide neatly into 2 types. Every book begins with basic definitions of smooth manifolds, tangent vectors and spaces, differentials/derivatives, immersions, embeddings, submersions, submanifolds, diffeomorphisms, and partitions of unity. Also the inverse function theorem is at least cited, if not proved (the proof is left to the reader here), as well as Sard's theorem and some sort of embedding theorem, usually Whitney's "easy" one. But beyond that the 2 types of books diverge, with one type treating vector bundles, the Frobenius theorem, differential forms, Stokes's theorem, and de Rham cohomology, and then possibly continuing on to differential geometry or Lie groups, such as in Lee's
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30 of 35 people found the following review helpful By A Customer on September 3, 2002
Format: Hardcover
I had to study this for my degree. It was one of those books that one person bought and was passed around mainly due to it's outrageous cost. It has a lack of rigour that is not made up by being more intuitive or giving the reader insight into why differential topology is such a great subject.
Transversality is rightly given prominence, but you don't really walk away with a good feel for it's importance or power. Degrees, linking numbers etc I got for 10 GBP with Milnor's Topology from a Differential Point of View.
As an introduction to differential topology - with a little point set and alot of algebraic throw in - Bredon's Geometry and Topology sets the gold standard, with Darling's Differential Forms and Connections doing a good job on the differential geometry front and Milnor's book above providing bedtime reading beforehand. You can buy all three together for around the same price as this book.
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22 of 25 people found the following review helpful By Adrian Jenkins on July 13, 2004
Format: Hardcover
First, I must comment about the reviewer below (who is obviously a greater mathematician than I) - I wouldn't recommend Bredon's book to anyone who wants to study differential topology. Man, I fought through a year of algebraic topology with that book, and I'm not sure I got a darn thing out of it! Being of a more analytic, geometric mindset, however, Guillemin and Pollack's book was right up my alley.
First, the authors make the wonderful assumption in the beginning that all manifolds live in R^n for some large enough n. This made study a great deal easier for me, as fighting through charts and atlases may not be the best place to start manifold theory (I don't mean to shortchange other important methods for working with differentiable manifolds, but rather I want to emphasize that many students might get lost in the machinery before learning anything of the theory). The book moves casually along (as the authors suggest, this book is nice for a smell-the-flowers two semester grad school class; we finished in Wisconsin in about a semester and a half before moving on to other pastures). The authors' reluctance to mention functors is also quite nice (I have asked many an algebraic topologist to describe these little guys, and the best answer I've heard is "A functor is an arrow"). A bit of analysis knowledge is nice, particularly in chapter four, and linear algebra (which seems to be a lost art, at least over here in the states) is absolutely critical.
For those of you out there who want to learn a little of this vast and incredibly interesting subject, I would highly recommend this book (even over Milnor's "Topology from the Differential Viewpoint", although the price of Milnor is much nicer).
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10 of 10 people found the following review helpful By Lucius Schoenbaum on October 29, 2010
Format: Hardcover Verified Purchase
the AMS Chelsea edition appears to be a digital facsimile of the original with pixillated letters. the typeface is visibly deteriorated - a cleaner image comes from an ordinary laser printer. It's distracting when reading what I think is a very nice book.
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9 of 10 people found the following review helpful By Jairo S. Bochi on August 13, 2011
Format: Hardcover Verified Purchase
I loved to study this book several years ago as an undegraduate. Now I have to teach those subjects, so I decided to buy a copy for myself. I received the book, admired the beautiful hardcover, but when I opened it I was immediately shocked by the crude quality of the printing. The problem is that this is a poorly scanned version of the old edition (which I took from the library to compare). I fear I'll be dizzy if I start reading this; I guess that if I try to scan a page of the original with my home scanner and print it on a laser printer I'll get a better result. I'm very surprised that AMS published this. Now, for the first time in many years as a costumer, I'll try to return this book to Amazon.

PS: Another reviewer (Lucius Schoenbaum) had similar complaints as me, but for some reason he gave a 5 star rating. My single star refers not to the text itself, but to the quality of this printing and to the value of the purchase.
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