Characteristic Classes. (AM-76) [Paperback]

John Milnor (Author), James D. Stasheff (Author)

Product Details

• Paperback: 340 pages
• Publisher: Princeton University Press (August 1, 1974)
• Language: English
• ISBN-10: 0691081220
• ISBN-13: 978-0691081229
• Product Dimensions: 9.1 x 6.1 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.4 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #354,771 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

15 of 17 people found the following review helpful:

5.0 out of 5 stars Great!, June 6, 2002

By 

Alex "supermanifold" (MTL) - See all my reviews

This review is from: Characteristic Classes. (AM-76) (Paperback)

The point to be made here is that M&S and books comparable to it ( I can think of those by Morita, off hand) are written in a style amenable to mathematicians. The purely formal, albeit axiomatic, approach survives as it appeals more to purists than to physicists. There's really nothing lacking in MS: although dated, it's very readable, requiring only a minimum of prerequisites, and this is what makes it attractive, with an appeal to a wide spectrum of audiences. Physical applications are bountiful, and they can be sought elsewhere in the literature.

On the history of algebraic topology, have a look at the monographs of Dieudonne.

11 of 13 people found the following review helpful:

5.0 out of 5 stars Fantastic, April 26, 2000

By A Customer

This review is from: Characteristic Classes. (AM-76) (Paperback)

This is a wonderful book, both for the student and for the researcher. Whether you're an aspiring topologist or string theorist, you need this book. If you're a physicist, I would recommend Nakahara's book to supplement some of the discussions. This book progresses very nicely, gently easing you into things with some elementary topics early on, and then building up motivation and machinery as the more advanced topics are reached. You will almost definitely not be left confused or lost. Simply put, this is a classic that should reside on everyone's shelf.

24 of 31 people found the following review helpful:

5.0 out of 5 stars how many stars??, April 12, 2005

By 

mathwonk - See all my reviews

This review is from: Characteristic Classes. (AM-76) (Paperback)

I read this page to see how Milnor's book could average only 4 stars. I found two unfair, but intelligent, 2/3 star reviews apparently by physicists, miffed that a masterful 50 year old book on the foundations of the topic, does not provide a history of their invention, and a survey of their current use in physics. If a book serves its own and its author's purpose wonderfully well, but does not serve yours, that is your fault, not the author's. As a hint, it is in the Annals of Math series, not the Handbook for Physicists series. Please read the chapter on "obstructions", p. 139. There Milnor succintly provides exactly the interpretation requested, and a reference to the classic text by Steenrod.

The most important construction on a smooth manifold is its tangent bundle, and the basic question is whether smooth never zero vector fields exist. The subject begins with the theorem of Poincare & Hopf: a never zero vector field exists if and only if the topological euler characteristic of the underlying manifold is zero. For a polyhedron, this euler characteristic is the number V-E+F = vertices - edges + faces. Thus the most basic characteristic class is the euler class. Briefly, the others measure existence of sequences of independent vector fields. In 1957 their existence, construction and properties were clouded, and Milnor cleared this away once for all in these notes, published by demand and gratefully received by [almost] everyone. This is a great book, and a 2 star review only serves to rate ones own qualifications to appreciate it. I.e. these reviewers are rating not the book but its suitability for their own narrow interests. For another short introduction try the chapter in the book by Bott & Tu.