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A good book for an introduction to Algebraic Topology

  1. Jun 11, 2012 #1
    Hi everybody.

    Next year I will start an undergraduate course on algebraic topology.
    Which book would you suggest as a good introduction to this matter ?

    My first options are the following:

    1.- "A First Course in Algebraic Topology" by Czes Kosniowski

    2.- "Algebraic Topology: An Introduction", by W.S.Massey

    but I don't know whether they are comparable or there is one that is much better than the other.

    Then, I am also wondering to pick up "Topology", by J.R.Munkres.
    I think it covers general and algebraic topology, but I am afraid it is not a "introductory" textbook as Kosniowski and Massey.

    Thanks in advance for your suggestions.
  2. jcsd
  3. Jun 11, 2012 #2
  4. Jun 11, 2012 #3


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    massey is my favorite author in algebraic topology, but you should go to the library and see for yourself which is more readable.
  5. Jun 12, 2012 #4
    Thanks Vargo and mathwonk for your suggestions.
    I'll take a look on Kosniowski's, Massey's and Munkres's and I'll decide.
    Hatcher's is interesting, but a little away from the contents of my course.
  6. Jun 12, 2012 #5


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    what does your course cover?
  7. Jun 13, 2012 #6
    I personally preferred Bredon for his concise and elegant presentation of the subject, also he gives nice proofs without making use of spectral sequences. Hatcher is a really nice book too. For a theoretical physics approach (as for notation and usability) I'd suggest Dubrovin/Fomenko/Novikov.
    Ultimately, you should definitely go to the library and see by yourself which one is more suitable ;) Enjoy!
  8. Jun 13, 2012 #7
    I'd say Kosniowski is more elementary than Massey or Munkres. It is brief, and cover less material than the other two, but it does have a pretty good exposition of the subject, with a good balance of abstract idea and concrete examples.

    Massey should be good if you already familiear with some point-set topology as well. If you don't, Kosniowski has a nice treatment of point-set topology in first 1/4 of his book that is just enough to learn algebraic topology in either Kosniowski or Massey.

    I would avoid Munkres for algebraic topology, though. I found his chapters on algebraic topology (ESPECIALLY the covering space chapter) to be quite dry and unmotivated. His general topology section is quite well-written and comprehensive, so that's another resource for point-set topology if you need it (though you certainly don't need to read ALL the chapters in general topology, though!).
  9. Jun 13, 2012 #8
    My course is a one-year elementary introductory course, first half on general topology and second half on algebraic topology.

    So, from your comments, I think the best choice for my elementary level in this matter, will be, perhaps, Kosniowski-Munkres for general topology and Kosniowski-Massey-Munkres for algebraic topology.

    In the library I've picked up Kosniowski and I find it very readable. Massey is a little harder. I agree with PieceOfPi.

    Thanks again for your help.
  10. Jun 13, 2012 #9
    I find Hatcher to be much more readable than Massey if you haven't seen much graduate level algebra yet. Massey just throws around things like direct limits of groups and tor functors and expects you to know them, or at most gives a dry list of properties. Hatcher actually goes through and motivates the algebraic constructions from the ground.
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