  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.
