Floer cohomology of the Chiang Lagrangian

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 ${\mathbf{CP}}^3$ 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.

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

References in corpus (2)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• The monotone wrapped Fukaya category and the open-closed string map

Cited by in corpus (1)

• Floer cohomologies of non-torus fibers of the Gelfand-Cetlin system