Math 6510 • Differentiable Manifolds

\begin{enumerate}
\item[(a)] State Stokes theorem.
\item[(b)] If \(\omega\in\Omega^n(\R^n)\) has compact support and
\(\int_{\R^n}\omega\ne0\) show that there does not exist an
\(\alpha\in\Omega^{n-1}(\R^n)\) with compact support and \(d\alpha=\omega\).
\item[(c)] Now assume that \(n=1\) and that \(\int_{\R}\omega=0\). Find an
\(\alpha\in\Omega^0(\R)\) with compact support and \(d\alpha=\omega\).
\end{enumerate}