# Spherical Lagrangians via ball packings and symplectic cutting

```@article{Borman2014SphericalLV,
title={Spherical Lagrangians via ball packings and symplectic cutting},
author={Matthew Strom Borman and Tian-Jun Li and Weiwei Wu},
journal={Selecta Mathematica},
year={2014},
volume={20},
pages={261-283}
}```
• Published 26 November 2012
• Mathematics
• Selecta Mathematica
In this paper, we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, \$\$S^{2}\$\$ or \$\$\mathbb{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…
22 Citations

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