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I'm looking for an undergraduate-level introduction to homotopy theory.

I'd prefer a brief (<200pp.) book devoted solely/primarily to this topic. IOW, something in the spirit of the AMS Student Mathematical Library series, or the Dolciani Mathematical Expositions series, etc.

Edit: I'm looking for an "easy read", one that aims to give quickly to the reader a feel for the subject.

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5 Answers 5

up vote 3 down vote accepted

I like Chapter 4 of Hatcher's book. Another source that is much less well-known is Philip R. Heath's book "An introduction to homotopy theory via groupoids and universal constructions". It is about 130 pages long and only assumes some point set topology and some idea of what a functor is, but no advanced category theory is used. It also has exercises inline with the text which is nice, and it has more of a homotopy flavour than Hatcher, which is more of a general algebraic topology text. I suggest you take a look at both and see which one you might like to read.

An alternative is Brayton Gray's book "Homotopy Theory", though it is over 200 pages and definitely tougher going with tons of technical proofs.

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My favorite ~200 page introduction to homotopy theory: http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf. You can find a physical copy on Amazon for relatively cheap as well.

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4  
That might be a bit difficult for the student, Dori. –  Mathemagician1234 Dec 24 '13 at 19:30
    
Thats true. It is not an easy book and definitely depends on the level of the student but there are undergrad students who could do it and benefit a lot from it with hard work. –  Dori Bejleri Dec 24 '13 at 20:28

A canonical choice would be Algebraic Topology, A.Hatcher.

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You should have a look at "Algebraic Topology from a Homotopical Viewpoint" by Aguilar, Gitler and Prieto, it might be what you are looking for!

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I would strongly recommend the book of A. Hatcher, which is available for free in his webpage.

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