= Compact first-cohomology obstruction to a Lagrangian fibration
{title2=$H^1(L;\mathbb R)=0$}
A compact <Lagrangian submanifold> $L$ with vanishing first <de Rham cohomology> cannot be a fibre of a smooth positive-dimensional <fiber bundle> whose nearby fibres are also <Lagrangian submanifolds>. In a <Weinstein neighborhood>, nearby fibres are <one-form graphs> of closed forms. They are exact by the <cohomology> assumption, so meet the <zero section> at a critical point of their potential, contradicting disjointness of distinct fibres.
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