Rational Lagrangian submanifold (source code)

= Rational Lagrangian submanifold

For a <Lagrangian submanifold> $L$ in an exact symplectic manifold with primitive $\lambda$, its period subgroup is $\{\int_c\lambda:c\in H_1(L;\mathbb Z)\}\subset\mathbb R$. It is rational when this subgroup is discrete. If it is nonzero, it is $\gamma\mathbb Z$ for a unique $\gamma>0$. Some conventions reserve the word rational for this nonzero case. The zero subgroup corresponds to an <exact differential form> $\lambda|_L$; its least positive period is interpreted as $+\infty$ if that endpoint convention is admitted.