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Can anyone tell me why it is that Lie groups seem to have their second fundamental group $\pi_2(G)$ equal to $0$, or provide me with a link to an article or a book reference?

I came across this fact reading an article where the author considers principal $G$ bundles with $G$ a simply connected simple group.

thank you

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For complex reductive groups, one can reduce to its maximal compact subgroup. See GTM98, p.153, p.225. – shenghao Mar 17 '11 at 0:50
up vote 3 down vote accepted

See: Homotopy groups of Lie groups

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