Remark

Tag 01CB, permanent. Cite it as [Bourbaki, Tag 01CB].

Lie Groups and Lie Algebras, chapter IX, § 4. Root system associated to a compact group

It can be shown (cf. Exercise 2 of §5) that $\pi_2(G/H)$ is zero. The exactness of the preceding sequence then gives an isomorphism from $\pi_2(G/H)$ to $N(G,T)/N(H,T)$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Exercise 2 of §5)