Math 6510 • Differentiable Manifolds

Let \(\omega\) and \(\eta\) be two differential forms on a manifold \(M\) .
\begin{enumerate}

\item
Define the wedge product \(\omega \wedge \eta\).


\item
Prove that if \(\omega\) and \(\eta\) are both closed then so is \(\omega \wedge \eta\).


\item
Prove that the de Rham cohomology class of \(\omega \wedge \eta\) is unchanged
if \(\omega\) and \(\eta\) are replaced by different representatives of the same
cohomology classes.
You are allowed to use the identity relating exterior differentiation and
wedge product, but you should state it carefully.

\end{enumerate}