Customer Reviews

An Introduction to Algebraic Topology (Graduate Texts in Mathematics)

5 star:		(2)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

Rotman's book presents all the material one would expect of an introductory text, in the language of Categories although still accessible to those who have never seen categories before. While Rotman's style and exposition is excellent, the book often gets bogged down in cumbersome notation. Also some other textbooks(e.g. Munkres Elements of Algebraic Topology) give more motivation to the material and explain what is actually going on geometrically(as opposed to algebraically). Also, the exercises are generally quite easy. Overall, I recommend Rotmans book to people who don't mind being patient, and waiting to see the whole picture.

Each text that I have read by Rotman is logically sound, well thought out, there are ample explanations, exercises as well as examples, and moreover, Rotman does an excellent job proving results. Sure he leaves the reader to prove certain results but, in general, all major concepts he will prove or, when it comes to familiar sticking points for students, Rotman will show that reader how to effectively prove these types of results. Now, Algebraic Topology is not an easy subject (actually it is a beautiful and far-reaching subject) and, depending upon the authors approach, the level of 'mathematical' maturity required can quickly escalate. Rotman's text is just above middle of the road with respect to this proverbial and undefined notion-'mathematical maturity'. Not as far-off as Spanier and not quite as gentle as Hatcher. For the reader who has this maturity or the necessary background, then Rotman's text is a must read provided you enjoy texts that follow the theorem-proof-theorem format. Furthermore, the logical consistecny with respect to how and when material is present to the reader places this text in a league of it's own. Without a doubt I could imagine any beginning graduate student or confident undergradute tackling this text on their own. For example, I am no math wizard but with only a background consisting of point-set topology with an introduction to the Fundamental Group, Abstract Algebra (Hungerford style) and Analysis (Rudin style) I was able to begin reading and, in particular, solving problems from Rotman's text while a senior undergraduate. For those of you who would like to learn the subject and learn it well but who are scared of this text (Springer can do that to people) I wouls strongly recommend pairing this text with Allen Hatchers or Part II of James Munkres' text depending on your level of enjoyment with respect to suffering your way through texts. In fact, I would suggest reading Munkres in its entirety since, this approach would properly prepare your for Rotman's text and the transition would be seamless. Finally, if, while reading this text you find yourself feeling lost during the initial chapters due to the use of Category Theory, I would suggest pushing forward and not becoming too hung up on acquirring a 'total' understanding. Things will make more sense as you progress through the later chapters. Enjoy and good luck!

5 April 2011 - Updated to 5 stars: I must have fell asleep at the wheel when aiming for the stars.

It seems Allen Hatcher book is going to be the standard in AT
I strongly feel ¡¡ What a pity¡¡

The Rotman books is much much clearer and better, then my advice is

If you can afford the cost give up Hatcher's and get Rotman's