Recent content by Sephi

I'm currently learning some homology theory but I have some difficulties computing homology groups of a few simple spaces. If someone could do the explicit calculation for RP(2), it would be really nice. Thank you :)

But such vector field doesn't exist on S². It's the statement of the hairy ball theorem : there is no non-vanishing vector field on S^{\ n} if n is even. Actually, I'm trying to prove that theorem for n=2, but only with the tools I presented in the first message (and I know it's possible).

I think it would. A section of TS² is a vector field on S². If TS² is trivial, then there exists at least one vector field without a zero. Thus, if we can prove that such vector field does not exist on S², it would mean that TS² is non trivial. But I don't know how to proceed, by using the...

Hi everybody, How can one show that the tangent bundle TS² of the 2-sphere is not trivial ? I know we can use the tools of algebraic topology, but I'm looking for a way to show it only with elementary tools of differential geometry. More precisely, I constructed an atlas for TS² by using the...

Hi people, I'm learning differential geometry in a book (Intro to smooth manifolds, by John Lee) and I have some difficulties with the tangent distributions. Actually, I don't know what to do if, given a distribution spanned by some vectors fields, I want to find its integral manifolds. Can...