The group of homotopy classes of loops at a basepoint x₀ under concatenation. Captures the '1-dimensional holes' of X. π₁(S¹) = ℤ.
Fundamental group π₁(X, x₀)
Related concepts
- Continuous map
- Homotopy
- Topological space
- Group (G, ·)
- Homotopy group π_n(X)
- Covering space
- Monodromy
- Covering space theory
- Seifert-Van Kampen theorem
- Hairy ball theorem
- 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}
- Granular physics
- Catenanes & mechanical bonds
- Extended evolutionary synthesis