Rod-like molecules align with a director field n̂. Topological defects with half-integer winding numbers cannot be removed by continuous deformations.
Click to add +½ defect, Right-click to add −½ defect, Middle-click to add +1 defect
Frank elastic energy: F = ½K∫[(∇·n̂)² + (n̂×(∇×n̂))²]d²r. Defects of charge +½ and −½ attract and annihilate. The sum of topological charges must equal 0 for flat geometry (disc topology). These topological defects appear in biological active matter — cell layers, bacterial colonies.