  Time-dependent systems have recently been shown to support novel types of
topological order that cannot be realised in static systems. In this paper, we
consider a range of time-dependent, interacting systems in one dimension that
are protected by an Abelian symmetry group. We classify the distinct
topological phases that can exist in this setting and find that they may be
described by a bulk invariant associated with the unitary evolution of the
closed system. In the open system, nontrivial phases correspond to the
appearance of edge modes in the many-body quasienergy spectrum, which relate to
the bulk invariant through a form of bulk-edge correspondence. We introduce
simple models which realise nontrivial dynamical phases in a number of cases,
and outline a loop construction that can be used to generate such phases more
generally.
