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I try to understand why for a connected Lie group $G$ the first fundamental group $\pi_1(G)$ is abelian, and mainly why the second fundamental group is trivial $\pi_2(G)=0$?

Thanks for anyone who give me references for a 'simple proof' of these results

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Some references:

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Many thanks Willie, for the nice links. For $\pi_2(G)=0$ I guess there is no simple proof! :(( – amine Sep 4 '11 at 10:35

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