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Topology and Geometry (Graduate Texts in Mathematics)

by: Glen E. Bredon
 | Springer

0387979263  9780387979267 

Topology and Geometry (Graduate Texts in Mathematics)
By Glen E. Bredon




Product Description:

This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all topologists will want students to see, including surfaces, Lie groups and fibre bundle theory. With a thoroughly modern point of view, it is the first truly new textbook in topology since Spanier, almost 25 years ago. Although the book is comprehensive, there is no attempt made to present the material in excessive generality, except where generality improves the efficiency and clarity of the presentation.




Summary: a different perspective
Rating: 3

While I agree with reviewers generally that this is a good book, i should warn that bredon isnt for the faint of heart. He makes use of simple language from category theory, doesnt always completely introduce his discussions (see for example the chapter on the tangent bundle where tangent bundle is never defined), and some other things that are nuisances to the newcomer.

I do think this is a good modern readable textbook, but for the student who has a solid foundation in mathematics. I didnt find it as accessable as other topology books, say Hatcher or Lee's books (but lee's are not as complete).



Summary: excellent for first year graduate study
Rating: 5

This was the assigned book in my first year grad topology course. It has good examples, interesting exercises. I like the emphasis on geometrical examples, constructions. It's not easy to read, but interesting.



Summary: Among the best textbooks in algebraic topology.
Rating: 5

As the previous reviewers have commented, this book is very accessible and detailed. I should add that the authour never lets you get lost in the labyrinth of abstract nonsense; the treatment is always geometric rather than homologico-algebraic. The only complaint I have is, the book would be more useful with chapters on spectral sequences, cobordism and K-theory.



Summary: The Graduate Sudent's Topology Bible
Rating: 5

If you want to learn topology, this book is the place. Though this text can require some maturity, the range of topics and the clarity of exposition are outstanding. My only complaint is that an additional appendix covering the basics of category theory would have been quite useful. Bredon not infrequently uses the language of category theory (though always in a non-essential way). Since this text is aimed at 1st year graduate students, I think the tacit assumption that the student has already encountered these topics is not justified. That such a minor point is my chief complaint speaks volumes of my esteem for this text.



Summary: My secret weapon in topology
Rating: 5

Today I told someone that Bredon's "Topology and Geometry" book was my secret weapon. I say this because it has mostly everything a grad student in topology needs to know in order to be fluent in the subject. I bought it not because I was taking a class from it--I got it because I saw it at the library and realized that this is the 'end all' topology book for me and that I will not need to buy all those 'other' books in topology anymore. I will warn you though--some of the proofs are terse, so you have to be somewhat 'mathematically mature'. It is definately harder than Munkres' "Topology: A first course" (the red book). But it goes beyond the point set crap that gets (in my opinion) too much airtime. I wish I would have taken a class under this book.