  We investigate the existence of topological phases in a dense two-dimensional
atomic lattice gas. The coupling of the atoms to the radiation field gives rise
to dissipation and a non-trivial coherent long-range exchange interaction whose
form goes beyond a simple power-law. The far-field terms of the potential --
which are particularly relevant for atomic separations comparable to the atomic
transition wavelength -- can give rise to energy spectra with one-sided
divergences in the Brillouin zone. The long-ranged character of the
interactions has another important consequence: it can break of the standard
bulk-boundary relation in topological insulators. We show that topological
properties such as the transport of an excitation along the edge of the lattice
are robust with respect to the presence of lattice defects and dissipation. The
latter is of particular relevance as dissipation and coherent interactions are
inevitably connected in our setting.
