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Apr 19, 2013 at 1:22 comment added Theo Johnson-Freyd Well, I mean, there are many applications of the general statement that $\pi_2$ is trivial. But for no $G$ can elements of $\pi_2(G)$ be applied to some particular construction, the way that $\pi_1$ or $\pi_3$ can.
Apr 18, 2013 at 4:35 comment added Qiaochu Yuan No applications? Isn't $\pi_2$ being trivial related to the Whitehead lemma?
Apr 18, 2013 at 4:00 history answered Theo Johnson-Freyd CC BY-SA 3.0