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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

flag	asked Mar 17 2011 at 0:39 Olivier Bégassat 921●6●17

For complex reductive groups, one can reduce to its maximal compact subgroup. See GTM98, p.153, p.225. – shenghao Mar 17 2011 at 0:50

Dick Palais · Accepted Answer · 2011-03-17 01:23:38Z UTC

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See: http://mathoverflow.net/questions/8957/homotopy-groups-of-lie-groups

answered Mar 17 2011 at 1:23

Dick Palais
10k●1●38●61

nullity of the second fundamental group of a Lie group

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