Spherical Lagrangians via ball packings and symplectic cutting

Matthew Strom Borman, Tian Jun Li, Weiwei Wu

Research output: Contribution to journalArticlepeer-review


In this paper, we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S2 or ℝℙ2, 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.

Original languageEnglish (US)
Pages (from-to)261-283
Number of pages23
JournalSelecta Mathematica, New Series
Issue number1
StatePublished - Jan 2014
Externally publishedYes


  • Lagrangian knots
  • Rational manifolds
  • Symplectic ball packing
  • Symplectic cutting
  • Symplectic manifolds

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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