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.
- What are the prerequisites for stable homotopy theory?
- Based on what I have learned, what text would you recommend for an introduction to stable homotopy theory?
- Do I have to study homology theory before stable homotopy?