Some Topological Considerations about Defects on Nematic Liquid Crystals

In this study, a nematic liquid crystal is used as an example to show analytically how an originally bi-dimensional system avoids a configuration with a singular pole. The system escapes into the third dimension with the simultaneous creation of a branch cut. It is presented an introductory study of some topological properties of defects in nematic liquid crystal. Special detach is given to the planar instabilities of these objects and to the corresponding properties of the escape into the third dimension of the disclinations with topological charge S=1 and S=1/2. As a final result we show that the tri-dimensional pole with charge S=1/2 is topological equivalent to the Möbius strip.