This paper is a continuation of our previous paper [RT]. In [RT], among other things, we gave a mathematical foundation to the theory of the quantum cohomology ring on semi-positive symplectic manifolds. We also defined higher genus symplectic invariants not coupled with gravity (topological sigma models) in terms of inhomogeneous holomorphic maps from a fixed Riemann surface, and proved that they satisfy a composition law. Topological gravity, first discussed by Witten, is related to intersection numbers in the moduli space of marked Riemann surfaces. Witten observed that a certain relation, suggested by the physical interpretation of the theory, might hold betwen those intersection numbers and the KdV hierarchy. This relation was clarfied by Kontsevich (cf. [Ko]).
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