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 [Chi04]. We prove that, if we work with coefficients in a field of characteristic 5, this Lagrangian has non-vanishing Floer cohomology and that it split-generates the Fukaya category.