Floer cohomology of the Chiang Lagrangian

2014/01/16 by J. D. Evans, Jonathan David Evans, Evans, Jonathan David +3 · 2 citations
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.GT #math.SG #msc:53D12 #msc:53D37 #msc:53D40

paper · pdf · doi:10.48550/arxiv.1401.4073

40 pages, 13 figures; v2 added computation of module structure and strong generation result, v3 incorporated referee's comments to agree with accepted version. To appear in Selecta Mathematica

arxiv created 2014/11/19 · arxiv updated 2014/11/20

Abstract

We study holomorphic discs with boundary on a Lagrangian submanifold L in a Kaehler manifold admitting a Hamiltonian action of a group K which has L 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 CP³ first noticed by Chiang. 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.

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• Floer cohomologies of non-torus fibers of the Gelfand-Cetlin system
• The existence criterion of holomorphic discs for higher A_∞ operations via minimal discs

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