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Jun 19, 2015 at 21:42 comment added Dylan Wilson To answer your last question, knowing about what all cohomology theories say about a space is the same as knowing its stable homotopy type. So you're asking "Are there good references for stable homotopy theory?" and the answer to that question is "Yes" :)
Jun 19, 2015 at 21:25 comment added Harrison Smith I'm accepting this answer because it's a good answer, and because it answers my main question, so thank you for that! That said, I'm still interested in the others!
Jun 19, 2015 at 21:23 vote accept Harrison Smith
Jun 19, 2015 at 21:23 vote accept Harrison Smith
Jun 19, 2015 at 21:23
Jun 19, 2015 at 21:12 history answered Dylan Wilson CC BY-SA 3.0