In this article, we make the first steps toward developing a theory of intersections of coisotropic submanifolds, similar to that for Lagrangian submanifolds.
For coisotropic submanifolds satisfying a certain stability requirement, we establish persistence of coisotropic intersections under Hamiltonian diffeomorphisms, akin to the Lagrangian intersection property. To be more specific, we prove that the displacement energy of a stable coisotropic submanifold is positive, provided that the ambient symplectic manifold meets some natural conditions. We also show that a displaceable, stable, coisotropic submanifold has nonzero Liouville class. This result further underlines the analogy between displacement properties of Lagrangian and coisotropic submanifolds
Viktor L. Ginzburg. "Coisotropic intersections." Duke Math. J. 140 (1) 111 - 163, 1 October 2007. https://doi.org/10.1215/S0012-7094-07-14014-6