Abstract

Recently, a BRST invariant formulation of several integrable equations, including KdV, mKdV, Calogero-KdV and H.Dym, was obtained, with an infinite sequence of BRST invariant quantities conserved. This formulation arises from the flatness connection condition that follows from the field equation of a BRST formulation of the two-dimensional BF topological theory. In this paper, we extend the analysis of the BRST invariant KdV-ghost system. We obtain the Hamiltonian and Poisson structures of the system and extend the KdV hierarchy, that is, the sub-hierarchy of the Kadomtsev–Petviashvili hierarchy, to a BRST invariant KdV-ghost hierarchy, with an infinite sequence of BRST invariant conserved quantities. We have then endowed the KdV hierarchy with a cohomological and topological structure. © 2025