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Currently I know nothing about stable homotopy theory other than that it originated from the Freudenthal suspension theorem. But I believe that the following are studied in this field: spectrum, generalized homology.

Background: I have been reading Tammo tom Dieck's Algebraic Topology and have finished most of Chapters 1-6 and 8. These include: classical results on fundamental group(oid)s, covering spaces; suspension/loop space, Puppe sequences, fibrations/cofibrations; homotopy groups, exact sequences, higher connectivity, homotopy excision (Blackers–Massey), Freudenthal suspension theorem, Hopf–Brouwer degree theorem, Brouwer fixed point theorem; CW complexes, cellular approximation, CW approximation, Eilenberg–Mac Lane spaces.

Questions:

  1. What are the prerequisites for stable homotopy theory?
  2. Based on what I have learned, what text would you recommend for an introduction to stable homotopy theory?
  3. Do I have to study homology theory before stable homotopy?
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    $\begingroup$ I was at this point a couple of months ago. I found Akhil Mathew's notes to be an extremely good reference with my background almost exactly the same as yours (plus a bit more on spectral sequences/(co)homology) going into the topic: math.uchicago.edu/~amathew/256y.pdf. $\endgroup$
    – Alvin Jin
    Dec 27, 2018 at 21:11
  • $\begingroup$ @AlvinJin I've looked into the notes and it seems that they require a bit more than my background... Any recommendations for books that fill in the gap? $\endgroup$
    – Yuxiao Xie
    Dec 28, 2018 at 7:38

1 Answer 1

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Here's what you're looking for, it also has the required background.

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    $\begingroup$ While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review $\endgroup$
    – amWhy
    Dec 27, 2018 at 21:28
  • $\begingroup$ My bad, next time i'll pay more attention $\endgroup$
    – Nnn
    Dec 28, 2018 at 14:52

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