Spherical Lagrangians via ball packings and symplectic cutting
Abstract
In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction this is a natural extension of McDuff's connectedness of ball packings in other settings and this result has applications to several different questions: smooth knotting and unknottedness results for spherical Lagrangians, the transitivity of the action of the symplectic Torelli group, classifying Lagrangian isotopy classes in the presence of knotting, and detecting Floer-theoretically essential Lagrangian tori in the del Pezzo surfaces.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2012
- arXiv:
- arXiv:1211.5952
- Bibcode:
- 2012arXiv1211.5952S
- Keywords:
-
- Mathematics - Symplectic Geometry;
- 53Dxx;
- 53D35;
- 53D12
- E-Print:
- 25 pages, 2 figures