Coisotropic rigidity and C0-symplectic geometry

Abstract

We prove that symplectic homeomorphisms, in the sense of the celebrated Gromov–Eliashberg Theorem, preserve coisotropic submanifolds and their characteristic foliations. This result generalizes the Gromov–Eliashberg theorem and demonstrates that previous rigidity results (on Lagrangians by Laudenbach and Sikorav, and on characteristics of hypersurfaces by Opshtein) are manifestations of a single rigidity phenomenon. To prove the above, we establish a $C^0$-dynamical property of coisotropic submanifolds which generalizes a foundational theorem in $C^0$-Hamiltonian dynamics: uniqueness of generators for continuous analogues of Hamiltonian flows.