Topological Rigidity and Non-Abelian defect junctions in chiral nematic systems with effective biaxial symmetry

We study topologically stable defect structures in systems where the defect line classification in three dimensions and associated algebra of interactions (the fundamental group) are governed by the non-Abelian 8-element group, the quaternions Q_8. The non-Abelian character of the defect algebra leads to a topological rigidity of bound defect pairs, and trivalent junctions which are the building blocks of multi-junction trivalent networks. We realize such structures in laboratory chiral nematics and analyze their behavior analytically, along with numerical modeling.