  Periodically driven (Floquet) crystals are described by their quasi-energy
spectrum. Their topological properties are characterized by invariants attached
to the gaps of this spectrum. In this article, we define such invariants in all
space dimensions, both in the case where no symmetry is present and in the case
where the unitary chiral symmetry is present. When no symmetry is present, a
$\mathbb{Z}$-valued invariant can be defined in each gap in all even space
dimensions. This invariant does not capture all the properties of a system
where chiral symmetry is present. In even space dimension, chiral symmetry puts
constraints on its values in different gaps. In odd space dimension, chiral
symmetry also enables to define a $\mathbb{Z}$-valued invariant, only in the
chiral gaps $0$ and $\pi$. We relate both gap invariants to the standard
invariants characterizing the quasi-energy bands of the system. Examples in one
and three dimensions are discussed.
