Local rigidity, symplectic homeomorphisms, and coisotropic submanifolds

Abstract

We introduce the notion of a point on a locally closed subset of a symplectic manifold being "locally rigid" with respect to that subset, prove that this notion is invariant under symplectic homeomorphisms, and show that coisotropic submanifolds are distinguished among all smooth submanifolds by the property that all of their points are locally rigid. This yields a simplified proof of the Humilière-Leclercq-Seyfaddini theorem on the $C^0$-rigidity of coisotropic submanifolds. Connections are also made to the "rigid locus" that has previously been used in the study of Chekanov-Hofer pseudometrics on orbits of closed subsets under the Hamiltonian diffeomorphism group.

arXiv comment10 pages. v2: minor edits

References in corpus (5)

• Coisotropic rigidity and C^0-symplectic geometry
• Observations on the Hofer distance between closed subsets
• Local rigidity, contact homeomorphisms, and conformal factors
• Closed exact Lagrangians in the symplectization of contact manifolds
• Displacement energy of compact Lagrangian submanifold from open subset

Cited by in corpus (2)

• Local rigidity, contact homeomorphisms, and conformal factors
• On the supports in the Humilière completion and $\gamma$-coisotropic sets