What is the second stiefel whitney class of SO(n)?

Question

$\omega_2(SO(n))=?$, that is, What is the second stiefel whitney class of SO(n)?

Eric O. Korman · Answer 1 · 2011-04-21 16:49:08Z

up vote 6 down vote

$SO(n)$ is a Lie group and so its tangent bundle is trivial. Thus $w_2(TSO(n)) = 0$.

answered Apr 21 '11 at 16:49

Eric O. Korman
7,5701731

	Thank you for your help. Furthermore, Is the Frame bundle of a spin manifold as a manifold spin? – Boh Liu Apr 22 '11 at 4:57
	@Boh Liu : You should ask this as a separate question, as it has little to do with the original one. – Raeder Apr 22 '11 at 18:04

1 Answer