Concise course in algebraic topology

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Jacob Lurie is currently teaching a course at Harvard about chromatic homotopy. He's posting his lecture notes , and Chris Schommer-Pries is also posting notes. The standard texts Hatcher, May, etc. That leaves another half-century of development. So, as a follow-up to first-year algebraic topology - still far from the cutting edge, but very relevant to reaching it - may I recommend reading some of the classic papers of the mid-twentieth century?


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Many are easy to find online. Several - no, many! For me, the material is the more exciting in the words of its discoverers. Many people will have their own favourites; my list is slanted towards differential topology. A couple by Serre. Kervaire-Milnor's Groups of homotopy spheres I essentially began surgery theory. Both are astonishingly far-seeing. After Peter May and Kate Ponto released their new book, there are very readable introductions to many of the topics on the "second level" of algebraic topology.

MA3403 Algebraic Topology - Fall 2018

There is a wonderful book on Cohomology Operations by Mosher and Tangora. It is thin and only discusses one topic , but very nice. There is a pretty good, and comprehensive book by Fomenko and Fuks or Fuchs? I've only seen the Russian version so I can't vouch for the translation. It's also not very well-known, and not very easy to find, which is a shame the Russian version is more obtainable.


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It has a lot of stuff, including one of the nicer introductions to spectral sequences although I don't know a single book that does this well. Serre's thesis is nice, Hatcher's notes are OK, but this seems to be a topic best learned in a good class.

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It's also very readable. Here's a review institutional access probably required with a description of its contents. Introduction to Stable homotopy theory. Prelude -- Classical homotopy theory pdf , 99 pages. Part 1 -- Stable homotopy theory.

Part 1. Part 2 -- Adams spectral sequences pdf , 56 pages. This introduces and then proceeds systematically via model categories. Full details and proofs are given. First of all I want to comment that beyond the two "standard textbooks" Andrew L. Besides this, I want to mention two more recent books:.

I learned -still and will be learning - the fundamentals of Algebraic topology from a professor at my University, Dr. Carlos Prieto. He is the co-author, along Dr. Samuel Gliter and Dr. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered.


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Ask Question. Asked 9 years, 6 months ago. Active 2 years, 3 months ago. Viewed 20k times. While I think I admire your zeal, it might be wise to take more pauses for breath, or indeed for new paragraphs. If such a thing doesn't exist, what should a good modern textbook contain? Don't have a link handy at the moment. Now I know that they do. I was quite disappointed given the price,but it does contain a lot of nice stuff not accessible in the usual textbook fare.

I just think it's ridiculous to pay 50 bucks for what's basically a glorified set of lecture notes.

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A Concise Course in Algebraic Topology : J. Peter May : : Blackwell's

The Fields Institute has a lot of nerve,really Peter May. For detailed information on who wrote what, click the date in the middle of the question. Incidentally, in view of the original question, I have no intention of retiring any time soon. I know it's proper in scientific circles to refer to professors by their first names in informal conversation.

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Description Product Details Click on the cover image above to read some pages of this book! In Stock. The Curve Shortening Problem. Amazing Area Mazes. Multivariable Calculus. Ramanujan's Lost Notebook Part V.

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