  The interplay between topological phases of matter and dissipative baths
constitutes an emergent research topic with links to condensed matter, photonic
crystals, cold atomic gases and quantum information. While recent studies
suggest that dissipative baths can induce topological phases in intrinsically
trivial quantum materials, the backaction of topological invariants on
dissipative baths is overlooked. By exploring this backaction for a
centrosymmetric Dirac insulator coupled to phonons, we show that the linewidths
of bulk optical phonons can contain generic features that reveal the topology
of the electronic structure. This result is the first known example where
topological phases of an open quantum system may be detected by measuring the
bulk properties of the surrounding environment.
