Click generators σᵢ to compose braids — visualize strand crossings
4
Identity (empty word)
The braid group Bₙ has generators σ₁,...,σₙ₋₁ where σᵢ crosses strand i over strand i+1. Relations: σᵢσⱼ=σⱼσᵢ for |i-j|≥2 (distant strands commute), and σᵢσᵢ₊₁σᵢ=σᵢ₊₁σᵢσᵢ₊₁ (Artin braid relation).
Braids arise in topology (knot theory — close a braid to get a knot), algebraic geometry (monodromy of algebraic functions), and quantum physics (non-abelian anyons for topological quantum computation).