  A quantum quench is a nonequilibrium dynamics governed by the unitary
evolution. We propose a two-band model whose quench dynamics is characterized
by an arbitrary Hopf number belonging to the homotopy group $\pi
_{3}(S^{2})=\mathbb{Z}$. When we quench a system from an insulator with the
Chern number $C_{i}\in \pi _{2}(S^{2})=\mathbb{Z}$ to another insulator with
the Chern number $C_{f} $, the preimage of the Hamiltonian vector forms links
having the Hopf number $C_{f}-C_{i}$. We also investigate a quantum-quench
dynamics for a four-band model carrying an arbitrary second-Chern number $N\in
\pi _{4}(S^{4})=\mathbb{Z}$, which can be realized by quenching a
three-dimensional topological insulator having the three-dimensional winding
number $N\in \pi _{3}(S^{3})=\mathbb{Z}$.
