  We analyze interacting ultra-cold bosonic atoms in a one-dimensional (1D)
super-lattice potential with alternating tunneling rates t_1 and t_2 and
inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger
(SSH) model. A Z2 topological order parameter is introduced which is quantized
for the Mott insulating (MI) phases. Depending on the ratio t_1/t_2 the n=1/2
MI phase is topologically non-trivial, which results in many-body edge states
at open boundaries. In contrast to the SSH model the bosonic counterpart lacks
chiral symmetry and the edge states are no longer mid-gap. This leads to a
generalization of the bulk-edge correspondence, which we discuss in detail. The
edge states can be observed in cold atom experiments by creating a step in the
effective confining potential, e.g. by a second heavy atom species, which leads
to an interface between two MI regions with filling n=1 and n=1/2. Shape and
energy of the edge states as well as conditions for their occupation are
determined analytically in the strong coupling limit and in general by
density-matrix renormalization group (DMRG) simulations.
