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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!

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    Are you intending to do any of your homework yourself or have you posted it all?2011-06-24
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    Sorry,I have thought these problems for a long time,but I can't find any idea, so I just have to find help...2011-06-25
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    Interesting question, btw (one in the title, I mean).2011-06-26

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