If $\omega$ is a closed $2$-form on $S^4$, how can I show the $4$-form $ \omega \wedge \omega$ vanishes somewhere on $S^4$? I am guessing that the fact we're talking about the $2$-form being closed, that this is the crux.
$4$-form $ \omega \wedge \omega$ vanishes on $S^4$
5
$\begingroup$
differential-topology
manifolds
differential-forms
symplectic-geometry
-
3The *symplectic-geometry* tag is a bit cryptic here :) But this is connected to the proof that $S^4$ is not a symplectic manifold. – 2012-05-06