Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (“hedgehogs”), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately 10−8 per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space. ∗E-mail: [email protected]