  We show how to define a dynamical topological invariant for general
one-dimensional topological systems after a quantum quench. Focusing on
two-band topological insulators, we demonstrate that the reduced momentum-time
manifold can be viewed as a series of submanifold $S^2$, and thus we are able
to define a dynamical topological invariant on each of the sphere. We also
unveil the intrinsic relation between the dynamical topological invariant and
the difference of topological invariant of the initial and final static
Hamiltonian. By considering some concrete examples, we illustrate the
calculation of the dynamical topological invariant and its geometrical meaning
explicitly.
