Interpretation of the Dispersion of the Electron States of High-$T_c$ Cuprate Superconductors Based on the Theory of Topological Resonance

The unusual dispersion of electron states in antinodal direction for $n_h\simeq \frac{1}{8}$ holes/copper is explained. In photoelectron excitations, transformations of the $\mathbf{k}$ space as a consequence of symmetry breaking proves to be an exceptional phenomenon distinctly reflected by the experiments. Paired photoelectron emissions are predicted that enable a new energetic upward shift termed as \emph{pair shake-up effect} which explains the experimentally observed sharp transition between non-dispersive and dispersive behaviour. The disappearance of antinodal states for ${\mathbf{k}}_{\mathrm{\mid }\mathrm{\mid }}ϵ[0,\pm \pi \mathrm{/}2]$ is explained.