Braid group as fundamental group: π₁(C_n(R²)) = B_n; Artin presentation with σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1}

Layer 1 — Physicsin the topological-quantum-computing subtree

Braid group as fundamental group of the unordered configuration space. Setup: n distinguishable (resp. indistinguishable) particles on the 2-plane live in the configuration space F_n(R²) = (R²)^n \ Δ (resp. C_n(R²) = F_n/S_n). The…

Related concepts

Fundamental group π₁(X, x₀)
Abelian anyon mutual-statistics phase: ψ(a↻b) = exp(2πi·θ)·ψ; Laughlin ν=1/3 gives θ = 1/3 (exp(2πi/3))

Explore Braid group as fundamental group: π₁(C_n(R²)) = B_n; Artin presentation with σ_i σ_{i+1} σ_i = σ_{i+1} σ_i σ_{i+1} on the interactive knowledge graph →