Soft topological objects in topological media

Topological invariants in terms of the Green's function in momentum and real space determine properties of smooth textures within topological media. In space dimension $d=1$ the topological invariant $N_3$ in terms of the Green's function $\mathcal G(\omega,k_x,x)$ determines the fermion number of the kink, while in space dimension $d=3$ the topological invariant $N_5$ in terms of the Green's function $\mathcal G(\omega,k_x,k_y,k_z,z)$ determines quantization of Hall conductivity in the soliton plane within the topological insulators.