Open Gromov-Witten invariants in general are not well-defined. We discuss in detail the enumerative numbers of the Clifford torus T2 in ℂP2. For cyclic A∞-algebras, we show that a certain generalized way of counting may be defined up to Hochschild or cyclic boundary elements. In particular we obtain a well-defined function on Hochschild or cyclic homology of a cyclic A∞-algebra, which is invariant under cyclic A∞ homomorphisms. We discuss the example of the Clifford torus T2 and compute the invariant for a specific cyclic cohomology class.
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