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Article Dans Une Revue Duke Mathematical Journal Année : 2015

Coisotropic rigidity and C^0-symplectic geometry

Résumé

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.

Dates et versions

hal-00985792 , version 1 (30-04-2014)

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Citer

Vincent Humilière, Rémi Leclercq, Sobhan Seyfaddini. Coisotropic rigidity and C^0-symplectic geometry. Duke Mathematical Journal, 2015, 164 (4), pp.767-799. ⟨10.1215/00127094-2881701⟩. ⟨hal-00985792⟩
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