Abstract
We prove a version of the Arnol’d conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian L which has non-zero Morse-Novikov homology for the restriction of the Lee form β cannot be disjoined from itself by a C0-small Hamiltonian isotopy. Furthermore for generic such isotopies the number of intersection points equals at least the sum of the free Betti numbers of the Morse-Novikov homology of β. We also give a short exposition of conformal symplectic geometry, aimed at readers who are familiar with (standard) symplectic or contact geometry.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 639-661 |
| Number of pages | 23 |
| Journal | Journal of Symplectic Geometry |
| Volume | 17 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2019 |
Funding
The authors thank Vestislav Apostolov and Franc¸ois Laudenbach for inspiring discussions. The first author benefited from the hospitality of several institutions and wishes to thank the institute Mittag-Leffler in Stockholm, CIRGET in Montréal and MIT in Cambridge for the nice work environment they provided. The second author would like to thank Universitéde Nantes and the Radcliffe Institute for Advanced Study for their pleasant work environments. B. Chantraine is partially supported by the ANR project COSPIN (ANR-13-JS01-0008-01) and the ERC starting grant Géodycon. E. Murphy is partially supported by NSF grant DMS-1510305 and a Sloan Research Fellowship.
ASJC Scopus subject areas
- Geometry and Topology