Hamiltonian formalism of Whitham-type hierarchies and topological Landau-Ginsburg models

We show that the bi-hamiltonian structure of the averaged Gelfand-Dikii hierarchy is involved in the Landau-Ginsburg topological models (for An-Series): the Casimirs for the first P.B. give the correct coupling parameters for the perturbed topological minimal model; the correspondence {coupling parameters} ~ {primary fields} is determined by the second P.B. The partition function (at the tree level) and the chiral algebra for LG models are calculated for any genus g.