Floer cohomology of the Chiang Lagrangian

Jonathan David Evans ^[1] ; Yankı Lekili ^[2]
1. [1] University College London
  
  University College London
  
  Reino Unido
2. [2] King's College London
  
  King's College London
  
  Reino Unido
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 21, Nº. 4, 2015, págs. 1361-1404
Idioma: inglés
Enlaces
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Resumen
- We study holomorphic discs with boundary on a Lagrangian submanifold LL in a symplectic manifold admitting a Hamiltonian action of a group KK which has LL as an orbit. We prove various transversality and classification results for such discs which we then apply to the case of a particular Lagrangian in CP3CP3 first noticed by Chiang (Int Math Res Not 45:2437–2441, 2004). We prove that this Lagrangian has non-vanishing Floer cohomology if and only if the coefficient ring has characteristic 5, in which case, it generates the split-closed derived Fukaya category as a triangulated category.