Symplectic orientation
= Symplectic orientation
{title2=$\omega^n>0$}
A <symplectic form> on a $2n$-dimensional <smooth manifold> determines the <orientation> in which the nowhere-zero <volume form> $\omega^n/n!$ is positive. Consequently every <symplectic manifold> is orientable. In dimension two this forbids a <symplectic form> on the <Möbius strip>.