FLOER COHOMOLOGY OF THE CHIANG LAGRANGIAN

ABSTRACT. We study holomorphic discs with boundary on a Lagrangian sub-manifold L in a Kähler 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 inCP3 first noticed by Chiang [13]. We prove that this Lagrangian has non-vanishing Floer cohomology if and only if the coefficient ring has characteristic 5, in which case it (strongly) generates the Fukaya category. 1