Frolicher structures, diffieties, and a formal KP hierarchy

Abstract

We propose a definition of a diffiety based on the theory of Frolicher structures. As a consequence, we obtain a natural Vinogradov sequence and, under the assumption of the existence of a suitable derivation, we can form on it a Kadomtsev-Petviashvili hierarchy which is well-posed.

To appear in Contemporary Mathematics (A.M. Vinogradov Memorial Volume)