1
$\begingroup$

Is there any direct way to prove that $n$-manifold is orientable? In AT we can just calculate $n$'th homology group and check whether it's $\mathbb Z$ or $0$. But I want a geometric method, using differential forms. Thanks!

  • 0
    Interesting question, btw (one in the title, I mean).2011-06-26

1 Answers 1

1

If you have a nowhere vanishing n-form, then the manifold is orientable.

  • 0
    @ Gr$i$gory :Yes ,here I use th$i$s co$n$d$i$tion.2012-02-23