The Lagrangian Cubic Equation

Let M be a closed symplectic manifold and L subset of M a Lagrangian submanifold. Denote by [L] the homology class induced by L viewed as a class in the quantum homology of M. This paper is concerned with properties and identities involving the class [L] in the quantum homology ring. We also study the relations between these identities and invariants of L coming from Lagrangian Floer theory. We pay special attention to the case when L is a Lagrangian sphere.