Crossings: 0 | Click generator buttons to build a braid word
The braid group Bₙ on n strands has generators σ₁,…,σₙ₋₁ (strand i crosses over i+1)
with relations σᵢσⱼ=σⱼσᵢ (|i−j|≥2) and σᵢσᵢ₊₁σᵢ=σᵢ₊₁σᵢσᵢ₊₁ (braid/Yang-Baxter relation).
The word problem — deciding if two words represent the same braid — was solved by
Garside (1969) via the fundamental element Δ. Closing the braid gives a link; the braid index
of a knot is the minimum number of strands needed (Birman-Menasco theorem).