01141nas a2200121   4500008004100000245008100041210006900122260002700191520059400218653007100812100002100883856011500904       2001                        en  d00aInverse Problem and Monodromy Data for Three-Dimensional Frobenius Manifolds0 aInverse Problem and Monodromy Data for ThreeDimensional Frobeniu  bRIMS, Kyoto University3 aWe study the inverse problem for semi-simple Frobenius manifolds of dimension 3 and we\r\nexplicitly compute a parametric form of the solutions of theWDVV equations in terms of Painlevé VI\r\ntranscendents. We show that the solutions are labeled by a set of monodromy data. We use our parametric\r\nform to explicitly construct polynomial and algebraic solutions and to derive the generating\r\nfunction of Gromov–Witten invariants of the quantum cohomology of the two-dimensional projective\r\nspace. The procedure is a relevant application of the theory of isomonodromic deformations.10aFrobenius Manifolds, Painleve Equations, Isomonodromy deformations1 aGuzzetti, Davide  uhttps://www.math.sissa.it/publication/inverse-problem-and-monodromy-data-three-dimensional-frobenius-manifolds