Immersed Lagrangian Floer cohomology via pearly trajectories

We define Lagrangian Floer cohomology over Z₂-coefficients by counting pearly trajectories for graded, exact Lagrangian immersions that satisfy a certain positivity condition on the index of the non-embedded points, and show that it is an invariant of the Lagrangian immersion under Hamiltonian deformations. We also show that it is naturally isomorphic to the Hamiltonian perturbed version of Lagrangian Floer cohomology as defined in [4]. As an application, we prove that the number of non-embedded points of such a Lagrangian in Cⁿ is no less than the sum of its Betti numbers.