# 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} }

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…

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