$C^0$-rigidity of characteristics in symplectic geometry

TL;DR

This paper proves that in symplectic geometry, a homeomorphism that preserves a smooth hypersurface also preserves its characteristic foliation, demonstrating a form of $C^0$-rigidity.

Contribution

It establishes a $C^0$-rigidity result for characteristic foliations under symplectic homeomorphisms, extending understanding of symplectic invariants.

Findings

Symplectic homeomorphisms preserving smooth hypersurfaces also preserve characteristic foliations.

The result applies in the context of Eliashberg-Gromov's symplectic homeomorphisms.

Provides new insights into the stability of characteristic foliations under $C^0$ limits.

Abstract

The paper concerns a $C^0$-rigidity result for the charcteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.