Cohomological obstruction to a Lagrangian section
= Cohomological obstruction to a Lagrangian section
{title2=$[\sigma]\ne0\Longrightarrow\text{no global Lagrangian section}$}
If $[\sigma]\ne0$ in <de Rham cohomology>, a <twisted cotangent symplectic form> has no <Lagrangian submanifold> whose projection is a <diffeomorphism> onto the entire base. Such a submanifold would be a global <one-form graph>, and the <twisted Lagrangian graph criterion> would make $\sigma$ exact.