Fragility And Persistence Of Leafwise Intersections

Keywords

Coisotropic submanifolds; Hamiltonian Seifert conjecture; 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 C0-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 C0-convergence of hypersurfaces, Hamiltonian diffeomorphic to each other, does not in general force C0-convergence of the characteristic foliations.

Publication Date

8-26-2015

Publication Title

Mathematische Zeitschrift

Volume

280

Issue

3-4

Number of Pages

989-1004

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00209-015-1459-y

Socpus ID

84937977240 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84937977240

This document is currently not available here.

Share

COinS