On the Maslov class rigidity for coisotropic submanifolds

We define the Maslov index of a loop tangent to the characteristic foliation of a coisotropic submanifold as the mean Conley–Zehnder index of a path in the group of linear symplectic transformations, incorporating the “rotation” of the tangent space of the leaf – this is the standard Lagrangian counterpart – and the holonomy of the characteristic foliation. Furthermore, we show that, with this definition, the Maslov class rigidity extends to the class of the so-called stable coisotropic submanifolds including Lagrangian tori and stable hypersurfaces.