The fundamental concepts of the homotopy theory of defects in liquid crystals and the results of experimental studies in this field are presented. The concepts of degeneracy space, homotopy groups, and topological charge, which are used for classifying the topologically stable inhomogeneous distributions in different liquid-crystalline phases are examined (uni and biaxial nematics, cholesterics, smectics, and columnar phases). Experimental data are given for the different mesophases on the structure and properties of dislocations, disclinations, point defects in the volume (hedgehogs) and on the surface of the medium (boojums), monopoles, domain formations, and solitons. Special attention is paid to the results of studies of defects in closed volumes (spherical drops, cylindrical capillaries), and to the connection between the topological charges of these defects and the character of the orientation of the molecules of the liquid crystal at the surface. A set of fundamentally new effects that can occur in studying the topological properties of defects in liquid crystals is discussed.

RT Journal
T1 Defects in liquid crystals: homotopy theory and experimental studies
A1 Kurik,M.V.
A1 Lavrentovich,O.D.
PB Physics-Uspekhi
PY 1988
FD 10 Mar, 1988
JF Physics-Uspekhi
JO Phys. Usp.
VO 31
IS 3
SP 196-224
DO 10.1070/PU1988v031n03ABEH005710
LK https://ufn.ru/en/articles/1988/3/b/