What is the best beginner's book on Algebraic Topology?

In summary, when looking for a book on Algebraic topology, Rotman, Munkres, Hatcher, Greenberg and Harper, Massey's "Algebraic Topology: An Introduction", and Hocking and Young's "Topology" are recommended options, with Massey's "Basic Course in Algebraic Topology" being a clear and understandable choice for beginners. Other suggested resources include books by Fulton and Spivak for homology theory, Massey's book on differential topology, and Artin and Braun's book (if able to read German).
  • #1
pivoxa15
2,255
1
I am looking for the most basic but rigorous to some extent book on Algebraic topology out there.
 
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  • #2
Rotman is good. I think Hatcher is really hard to follow, though others like him.
 
  • #3
Well, Munkres has been written for undergrads. the first part of the book is general topology and the second is algebraic topology.
 
  • #4
Greenberg and Harper has the virtue of not using too many words :wink:

I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.
 
  • #5
Chris Hillman said:
Greenberg and Harper has the virtue of not using too many words :wink:

I think Hatcher's beautiful book is an important addition to the roster, but probably that it is intended for students who aren't feeling overwhelmed.

I've got Greenberg and Harper beside me. It looks formidable/impossible due to as you say not many words.

I'm looking for a dummies book, if there is one.

Aren't you a physicst? If so which area in physics? You seem to be keen with maths as well?
 
  • #6
I would try Munkres.
 
  • #7
His 'Topology'?
 
  • #8
Of course.
 
  • #9
i think you are looking for "Algebraic Topology: An Introduction" by William S. Massey
 
  • #10
A classic in Dover reprint is Hocking and Young's "Topology". It is a clear introduction to point-set topology and algebraic topology at the level of a first undergraduate course on topology. It is similar in coverage to Munkres but I find H&Y to be more readable.
 
  • #11
A cheap and cheerful introduction is Wallace's Intro to Algebraic Topology (Dover, ~£7). I ordered a handful of Dover books a little while ago on subjects I was unfamiliar with. After some very casual reading, the book has managed to provide me with a grounding in basic algebraic topology. Lots of nice pictures, and the exercises are very routine (so much so that in many cases you needn't put pen to paper).
 
  • #12
ah, i meant A Basic Course in Algebraic Topology by William S. Massey, it is a revised and enhanced version of Algebraic Topology, an Introduction...
 
  • #13
Algebraic topology for dummies?
It's not!
 
  • #14
Btw, Munkres is an introduction to Algebraic topology.

After his take, one procceeds to Edwin Spanier (Though I haven't yet, and probably will not have time either way to finish Munkers and even starting Spanier).
 
  • #15
william massey is one of the very few writers on advanced mathematics i know of who has always been understandable to the beginner.

i have not read his book recommended above including an introduction to singular homology (basic course...) but in grad school his little book on the fundamental group was the only one i could understand, and later his book which serves as the first 5 chapters of "basic course.." on both fundamental group and classification of two manifolds, seemed like a playtime book.

homology theory is notoriously hard to make understandable, and i would suggest looking at books by fulton, and the chapter in spivak's differential geometry book vol 1, as well.

i also recommend massey's book on differential topology, first steps.

hocking and young is a very old fashioned book, which has much good classical material, but more on point set topology than you need in algebraic topology, and the point of view is not at all up to date.

all the professional algebraic topologists here love to use hatcher in their courses, but to me it is not that appealing. i liked vick, homology theory, as a student also.

spanier is very detailed and formidable, but excellent for those wishing to become professionals.

for beginners massey is hard to beat. if you read german there is also a fine book by artin and braun, which was apparently the model for the first part of greenberg's book.
 
  • #16
i also recommend massey's book on differential topology, first steps.

Should be Wallace; "Differential Topology, First Steps"?

Massey's "Basic Course..." is very nice indeed and almost certainly a better recommendation than Hocking and Young.
 

FAQ: What is the best beginner's book on Algebraic Topology?

1. What is algebraic topology and why is it important?

Algebraic topology is a branch of mathematics that deals with the study of topological spaces using algebraic tools. It is important because it allows us to classify and understand the properties of spaces by assigning algebraic structures to them.

2. What are the basic concepts and techniques used in algebraic topology?

Some of the basic concepts and techniques used in algebraic topology include homotopy, homology, cohomology, and fundamental groups. These tools help us to understand the properties of topological spaces and their invariants.

3. How does algebraic topology differ from other branches of topology?

Algebraic topology differs from other branches of topology in that it uses algebraic techniques to study topological spaces, whereas other branches may use geometric or analytical methods. This allows for a more rigorous and systematic approach to understanding topological spaces.

4. What are some real-world applications of algebraic topology?

Algebraic topology has applications in various fields such as physics, computer science, and engineering. It is used to study and model complex networks, analyze data and patterns, and solve optimization problems.

5. Can anyone learn algebraic topology, even if they are not a math genius?

Yes, anyone can learn algebraic topology with dedication and practice. It is a complex branch of mathematics, but with patience and perseverance, anyone can understand its concepts and techniques.

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