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Feb 15, 2015 at 4:09 history edited Qiaochu Yuan CC BY-SA 3.0
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Feb 15, 2015 at 2:17 comment added Qiaochu Yuan Oh, I'm sure the real topologists and geometers know the answer. That class in $H^8(X, \pi_7 F)$ might just be the class $p_1^2 - 4 p_2 + 8 e$ that appears in your question (and in particular it would be consistent with what little I know about the unstable homotopy groups of these spaces that $\pi_7 F \cong \mathbb{Z}$).
Feb 15, 2015 at 0:48 comment added Bilateral Thanks for the answer, I will think about at it. Could it be possible that this is an open question in mathematics?
Feb 14, 2015 at 22:53 history answered Qiaochu Yuan CC BY-SA 3.0