Topological character of excitations in strongly correlated electronic systems: Confinement and dimensional crossover

Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as elementary excitations. After a history introduction, we shall discuss the topological aspects of elementary excitations, especially the confinement and the dimensional D crossover. At higher D the topological requirements for the combined symmetry originate the spin- or charge-roton like excitations with charge- or spin- kinks localized in the core. In quasi 1D world they can be viewed as resulting from a spin-charge recombination due to the 3D confinement.