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arXiv · 1211.5952

Spherical Lagrangians via ball packings and symplectic cutting

Matthew Strom Borman·Tian-Jun Li·Weiwei Wu
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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.

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Matthew Strom Borman, Tian-Jun Li, Weiwei Wu. 2012-11-26. Spherical Lagrangians via ball packings and symplectic cutting. https://doi.org/10.1007/s00029-013-0120-z

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