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On connection between topological Landau-Ginzburg gravity and integrable systems

We study flows on the space of topological Landau-Ginzburg theories coupled to topological gravity. We argue that flows corresponding to gravitational descendants change the target space from a complex plane to a punctured complex plane and lead to the motion of punctures. It is shown that the evolution of the topological theory due to these flows is given by the dispersionless limit of KP hierarchy. We argue that the generating function of correlators in such theories is equal to the logarithm of the tau function of the generalized Kontsevich model.