English

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

Symplectic Geometry 2016-05-23 v2

Abstract

We prove here a quantitative hh-principle statement that applies to isotropic embeddings of discs. We then apply it to get C0C^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 C0C^0-rigidity result for the action of a symplectic homeomorphism on the reduction of a coisotropic submanifold.

Keywords

Cite

@article{arxiv.1603.02299,
  title  = {Quantitative $h$-principle for isotropic embeddings and applications to $C^0$-symplectic geometry},
  author = {Lev Buhovsky and Jaime Bustillo and Emmanuel Opshtein},
  journal= {arXiv preprint arXiv:1603.02299},
  year   = {2016}
}

Comments

The paper is withdrawn due to gaps in the proof of quantitative h-principle of isotropic discs (Theorem 2.1), and in the proof of Lemma 4.1 which is essential for the proof of one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