  Topological states of matter were first introduced for non-interacting
fermions on an infinite uniform lattice. Since then, substantial effort has
been made to generalize these concepts to more complex settings. Recently,
local markers have been developed that can describe the topological state of
systems without translational symmetry and well-defined gap. However, no local
marker for interacting matter has been proposed yet that is capable of directly
addressing an interacting system. Here we suggest such a many-body local marker
based on the single-particle Green's function. Using this marker we identify
topological transitions in finite lattices of a Chern insulator with Anderson
disorder and Hubbard interactions. Importantly, our proposal can be
straightforwardly generalised to non-equilibrium systems.
