Fragility and Persistence of Leafwise Intersections
Abstract
In this paper we study the question of fragility and robustness of leafwise intersections of coisotropic submanifolds. Namely, we construct a closed hypersurface and a sequence of Hamiltonians -converging to zero such that the hypersurface and its images have no leafwise intersections, showing that some form of the contact type condition on the hypersurface is necessary in several persistence results. In connection with recent results in continuous symplectic topology, we also show that -convergence of hypersurfaces, Hamiltonian diffeomorphic to each other, does not in general force -convergence of the characteristic foliations.
Keywords
Cite
@article{arxiv.1409.7746,
title = {Fragility and Persistence of Leafwise Intersections},
author = {Viktor L. Ginzburg and Basak Z. Gurel},
journal= {arXiv preprint arXiv:1409.7746},
year = {2014}
}
Comments
17 pages, 3 figures; we removed one of our results (a refinement of Moser's theorem on leafwise intersections) and its proof, since a stronger theorem is proved in arXiv:1408.4578