  Under non-equilibrium conditions, bosonic modes can become dynamically
unstable with an exponentially growing occupation. On the other hand,
topological band structures give rise to symmetry protected midgap states. In
this letter, we investigate the interplay of instability and topology. Thereby,
we establish a general relation between topology and instability under
ac-driving. We apply our findings to create dynamical instabilities which are
strongly localized at the boundaries of a finite-size system. As these
localized instabilities are protected by symmetry, they can be considered as
topological instabilities.
