Chapter 20: Braid Group

Abstract:

Let n ≥ 3. The braid group ℬ_n of n strings (or group of n braids) has n − 1 generators {σ₁, σ₂, … , σ_n−1} (pairwise distinct) satisfying the relations

where e is the identity element. Thus it is generated by elements σ_j (σ_j interchanges elements j and j + 1). Thus actually one should write σ₁₂, σ₂₃, … , σ_n−1n instead of σ₁, σ₂, … , σ_n−1. The braid group ℬ_n is a generalization of the permutation group…