Spherical Lagrangians via ball packings and symplectic cutting

• Matthew Strom Borman ^[1] ; Tian-Jun Li ^[2] ; Weiwei Wu ^[3]
  1. [1] University of Chicago

     University of Chicago

     City of Chicago, Estados Unidos

     
  2. [2] University of Minnesota

     University of Minnesota

     City of Minneapolis, Estados Unidos

     
  3. [3] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 1, 2014, págs. 261-283
• Idioma: inglés
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• Resumen

  • 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.