Abstract
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 G(ω,k_x,x) determines the fermion number of the 1D soliton, while in space dimension D=3 the topological invariant N_5 in terms of the Green's function G(ω,k_x,k_y,k_z,z) determines quantization of Hall conductivity in the soliton plane within the topological insulators.
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