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

  • $\begingroup$ For complex reductive groups, one can reduce to its maximal compact subgroup. See GTM98, p.153, p.225. $\endgroup$ – shenghao Mar 17 '11 at 0:50

See: Homotopy groups of Lie groups


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.