Coisotropic rigidity and C^0-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-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 analogs of Hamiltonian flows.

27 pages. v2. Significant reorganization of the paper, several typos and inaccuracies corrected after the refeering process. A theorem (Theorem 5, completing the study of C^0 dynamical properties of coisotropics) added. To appear in Duke Mathematical Journal

References in corpus (2)

• On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows
• Bounding Lagrangian widths via geodesic paths

Cited by in corpus (9)

• Persistent homology and Floer-Novikov theory
• Bounds on spectral norms and barcodes
• The action spectrum and C^0 symplectic topology
• A C^0 counterexample to the Arnold conjecture
• Coisotropic Ekeland-Hofer capacities
• Local rigidity, symplectic homeomorphisms, and coisotropic submanifolds
• Existence of pseudo-heavy fibers of moment maps
• $C^0$-rigidity of Poisson diffeomorphisms
• Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry-Mather theory