Quantitative $h$-principle for isotropic embeddings and applications to $C^0$-symplectic geometry

Abstract

We prove here a quantitative $h$-principle statement that applies to isotropic embeddings of discs. We then apply it to get $C^0$-flexibility and rigidity results in symplectic geometry. On the flexible side, we prove that a symplectic homeomorphism might take a symplectic disc to a smooth isotropic one. We also get a $C^0$-rigidity result for the action of a symplectic homeomorphism on the reduction of a coisotropic submanifold.

The paper is withdrawn due to gaps in the proof of quantitative h-principle of isotropic discs (Theorem 2.1), and in the proof of Lemma 4.1 which is essential for the proof of one of main results (Theorem 3)