A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
An Introduction to Algebraic Topology
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||
 Sell Back Your Copy for $21.43
Whether you buy it used on Amazon for $31.10 or somewhere else, you can sell it back through our Book Trade-In Program at the current price of $21.43.
Used Price$31.10
Trade-in Price$21.43
Price after
Trade-in$9.67 |
Book Description
Special Offers and Product Promotions
- Buy $50 in qualifying physical textbooks, get $5 in Amazon MP3 Credit. Here's how (restrictions apply)
Frequently Bought Together
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
|
Most Helpful Customer Reviews
14 of 15 people found the following review helpful:
4.0 out of 5 stars
Good textbook,
By A Customer
This review is from: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (Hardcover)
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.
10 of 11 people found the following review helpful:
5.0 out of 5 stars
Rotman does it again.,
By
This review is from: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (Hardcover)
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.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
A readable alternative to Hatcher,
By
This review is from: An Introduction to Algebraic Topology (Graduate Texts in Mathematics) (Hardcover)
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
Share your thoughts with other customers: Create your own review
|
|
Inside This Book
(learn more)
First Sentence:
One expects algebraic topology to be a mixture of algebra and topology, and that is exactly what it is. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
covering homotopy lemma, natural chain equivalence, closed edge path, oriented simplicial complex, path connected implies, weak fibration, admissible open set, affine independent subset, natural chain map, lifting criterion, cogroup object, homotopy lifting property with respect, relative homeomorphism, same homology groups, regular covering space, level homotopy, gluing lemma, free chain complex, same homotopy type, cellular filtration, homotopy axiom, admissible neighborhood, full subcomplex, acyclic models, connected simplicial complex Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exact Homology Sequences, Seifert-van Kampen New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
One expects algebraic topology to be a mixture of algebra and topology, and that is exactly what it is. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
covering homotopy lemma, natural chain equivalence, closed edge path, oriented simplicial complex, path connected implies, weak fibration, admissible open set, affine independent subset, natural chain map, lifting criterion, cogroup object, homotopy lifting property with respect, relative homeomorphism, same homology groups, regular covering space, level homotopy, gluing lemma, free chain complex, same homotopy type, cellular filtration, homotopy axiom, admissible neighborhood, full subcomplex, acyclic models, connected simplicial complex Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exact Homology Sequences, Seifert-van Kampen New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
See all 100 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Cohomology of Groups (Graduate Texts in Mathematics, No. 87) by Kenneth S. Brown in Back Matter (1), and Back Matter (2)
- Elliptic Curves: Diophantine Analysis (Grundlehren der mathematischen Wissenschaften) by S. Lang in Back Matter (1), and Back Matter (2)
- Elements of Homotopy Theory (Graduate Texts in Mathematics) by George W. Whitehead in Back Matter (1), and Back Matter (2)
- Foundations of Differentiable Manifolds and Lie Groups (Graduate Texts in Mathematics) (v. 94) by Frank W. Warner in Back Matter (1), and Back Matter (2)
See all 100 books this book cites
- An Introduction to the Theory of Groups by Joseph J. Rotman on page 497, Back Matter (1), and Back Matter (2)
- An Introduction to Markov Processes (Graduate Texts in Mathematics) by Daniel W. Stroock in Back Matter (1), and Back Matter (2)
- Functions of One Complex Variable II (Graduate Texts in Mathematics) (Pt. 2) by John B. Conway in Back Matter (1), and Back Matter (2)
- Probability Theory II (Graduate Texts in Mathematics) by M. Loeve in Back Matter (1), and Back Matter (2)
- Number Theory in Function Fields by Michael Rosen in Back Matter (1), and Back Matter (2)
See all 100 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
