Bosons in a one dimensional chain can form two gapped phases
at integer filling, the Mott and Haldane insulators. The
critical point separating these two phases is gapped out by
a perturbation breaking lattice inversion symmetry. I will
show that encircling the critical point adiabatically in the
plane of the tuning parameter and the inversion symmetry
breaking perturbation, entails pumping of exactly one boson
across the Bose insulator. When multiple chains are coupled,
the two insulating phases are no longer sharply distinct,
but the pumping property survives and allows to define a
topological flux associated with gapless regions in the
phase diagram. This leads to strict constraints on the
topology of the phase diagram of systems of quasi-one
dimensional interacting bosons. Finally I will use the
pumping property to elucidate the topological invariant
underlying the Haldane phase and to discuss possible
extensions to interacting topological phases in higher
dimensions.