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

Topologically nontrivial states are common in symmetry broken phases at mac roscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as elementary excitations. After a history introducti on, we shall discuss the topological aspects of elementary excitations, esp ecially the confinement and the dimensional D crossover. At higher D the to pological requirements for the combined symmetry originate the spin- or cha rge-roton like excitations with charge- or spin- kinks localized in the cor e. In quasi 1D world they can be viewed as resulting from a spin-charge rec ombination due to the 3D confinement.