This paper describes the topologically possible global defect behavior of ordinary nematics in 3-space. It is written for physicists interested in defects of ordered media as well as for topologists, but instead of using an ‘intermediate’ way of presentation, which might appeal to no one, we first state the result for physicists and then, discussing the proof, turn to mathematicians and physicists who are inclined to read a mathematical paper.
AMS (MOS) subject classifications (1980)
82A99 57R25 57M25
Defects in ordered media nematic liquids linking numbers Poincaré-Hopf theorems