Resumen de Spherical Lagrangians via ball packings and symplectic cutting
Matthew Strom Borman, Tian-Jun Li, Weiwei Wu
In this paper, we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S2S2 or RP2RP2 , 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.
