  The topological classification of electronic band structures is based on
symmetry properties of Bloch eigenstates of single-particle Hamiltonians. In
parallel, topological field theory has opened the doors to the formulation and
characterization of non-trivial phases of matter driven by strong
electron-electron interaction. Even though important examples of topological
Mott insulators have been constructed, the relevance of the underlying
non-interacting band topology to the physics of the Mott phase has remained
unexplored. Here, we show that the momentum structure of the Green's function
zeros defining the ``Luttinger surface" provides a topological characterization
of the Mott phase related, in the simplest description, to the one of the
single-particle electronic dispersion. Considerations on the zeros lead to the
prediction of new phenomena: a topological Mott insulator with an inverted gap
for the bulk zeros must possess gapless zeros at the boundary, which behave as
a form of ``topological antimatter'' annihilating conventional edge states.
Placing band and Mott topological insulators in contact produces distinctive
observable signatures at the interface, revealing the otherwise
spectroscopically elusive Green's function zeros.
