String equation and quantum cohomology for noncompact symplectic manifolds (Q1876879)

In this note the author continues to investigate the properties of the Gromov-Witten invariants of noncompact, geometrically bounded symplectic varieties, which he had defined in [\textit{G.~Lu}, C. R. Math. Acad. Sci. Paris 338, No. 11, 885--888 (2004; Zbl 1057.53054)]. He defines gravitational correlators with coefficients in the Novikov ring, and proves that their generating function fulfills the generalized string and dilaton equations. In the case of compact symplectic manifolds, the result is due to [\textit{Y.~Ruan} and \textit{G.~Tian}, Invent. Math. 130, No. 3, 455--516 (1997; Zbl 0904.58066)]. Under the further assumption that the cohomology of the manifold is finite dimensional, the author proves that the Gromov-Witten potential obeys the WDVV equation, so that is possible to define a quantum ring structure on the cohomology.