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.
Keywords
Cite
@article{arxiv.1211.5952,
title = {Spherical Lagrangians via ball packings and symplectic cutting},
author = {Matthew Strom Borman and Tian-Jun Li and Weiwei Wu},
journal= {arXiv preprint arXiv:1211.5952},
year = {2014}
}
Comments
25 pages, 2 figures; v2: minor corrections and clarifications, added discussion after Corollary 1.2. To appear in Selecta Mathematica