  A universal feature of topological insulators is that they cannot be
adiabatically connected to an atomic limit, where individual lattice sites are
completely decoupled. This property is intimately related to a topological
obstruction to constructing a localized Wannier function from Bloch states of
an insulator. Here we generalize this characterization of topological phases
toward periodically driven systems. We show that nontrivial connectivity of
hybrid Wannier centers in momentum space and time can characterize various
types of topology in periodically driven systems, which include Floquet
topological insulators, anomalous Floquet topological insulators with
micromotion-induced boundary states, and gapless Floquet states realized with
topological Floquet operators. In particular, nontrivial time dependence of
hybrid Wannier centers indicates impossibility of continuous deformation of a
driven system into an undriven insulator, and a topological Floquet operator
implies an obstruction to constructing a generalized Wannier function which is
localized in real and frequency spaces. Our results pave a way to a unified
understanding of topological states in periodically driven systems as a
topological obstruction in Floquet states.
