Hello

I was asked in a test to do an integration of an exact form on a manifold. The first thing you think is to apply the Stokes theorem. The problem here is to determine the boundary of the manifold. Let and let . Now, is the boundary of the component of , such that , empty?

My teacher says it's not empty, but a fellow PhD of mine says it's empty. I don't know who's right. Can anyone find a way to decide this without any doubt remaining?

Thanks in advance.