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.
Cite
@article{arxiv.1305.1287,
title = {Coisotropic rigidity and C^0-symplectic geometry},
author = {Vincent Humilière and Rémi Leclercq and Sobhan Seyfaddini},
journal= {arXiv preprint arXiv:1305.1287},
year = {2015}
}
Comments
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