Lecture Notes on Elementary Topology and Geometry. [Paperback]

I. M. Singer (Author), J. A. Thorpe (Author)

Product Details

• Paperback: 214 pages
• Publisher: Scott, Foresman (1967)
• Language: English
• ASIN: B000NPSRVG
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #3,245,034 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

14 of 18 people found the following review helpful:

4.0 out of 5 stars Concise and modern, June 6, 2004

By A Customer

This review is from: Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics) (Hardcover)

First, a small carp at Amazon: The book has two authors and since John Thorpe is the junior and by far the less famous, I suspect that he actually did most of the writing. Please give him his due!

This is a very dense book. While this makes for rough sledding for the first timer, it's also an exciting introduction to modern topology and geometry and a good first step for those interested in such things in physics as gauge theories and superstrings. It's worth the effort.

Starting with the basics of set theory, the first couple chapters take the reader through point set topology. The next couple chapters introduce algebraic topology. The rest of the book is about the algebraic topology of differentiable manifolds and a very clean, modern introduction to the classical differential geometry of surfaces. The only caveat is, as Spivak says, "a weird proof of the de Rham theorem" in Chapter 6. I'm torn about this. The proof in Warner's "Foundations of Differentiable Manifold and Lie Groups" is much cleaner and better lends itself to other applications, but involves lots of machinery. The proof in Singer and Thorpe is a lot less elegant, using the lowest level tools possible. This makes the learning curve shorter and may make the theorem more clear, but may also obscure the big picture. Much of the important work in algebraic topology over the next 20 years and theoretical physics up to now is related to this result. Though much of this work was developed by Singer with his collaborater Michael Atiyah, their approach is closer to Warner's than to that in Singer and Thorpe.

For any particular topic in this book, you can find sources that you'll undoubtably find more digestible. This is the only book that brings them all together. It's an audacious effort.

4 of 4 people found the following review helpful:

4.0 out of 5 stars Nice overview of Point-Set, Algebraic, and Differential Topology, October 18, 2007

By 

Michael C. Wilson (Berkeley, CA) - See all my reviews
(REAL NAME)   

This review is from: Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics) (Hardcover)

I believe that one of the authors, I. Singer is a Fields Medalist, so this is co-written by one of the masters in the subject. It is one of the few books I'm aware of that covers point-set, algebraic, and differential topology. However, this is not in any way an exhaustive text. It is very spare and to the point. This is a small book packed with information. No exercises are included. It is not particularly advance in any one area of topology, so keep in mind that this is just an overview of all the main areas. However, just because it is not particularly advanced, does not mean it is easy to read for someone completely unfamiliar with the material. I tried reading the early chapters as a first introduction to topology, and didn't know what was going on. Reading of it got better when I read it side-by-side with the books by Munkres and Armstrong. This book is pretty abstract and dense, so it will read slowly. A lot of the finer details in the subjects are found in other texts.