Résumé
The line defects of three dimensional uniaxial nematics have a simple abelian algebra governing their interactions and so simply pass through one another. I will discuss, instead, biaxial nematics for which the fundamental group is non-abelian. As a result they exhibit topological entanglement/rigidity, trivalent junctions and associated networks, and stable bound states of pairs of disclinations. They can be experimentally realized in chiral nematics or in hybrid molecular-colloidal systems, realizing the notion of topological rigidity envisaged 50 years ago by Poenaru and Toulouse.
