Fundamental group (intro)
General · Mathematics
Study notes
Q: What is π₁(S¹)? Show loop winding twice is nontrivial. π₁(S¹) = ℤ (winding numbers!)! Loop γ(t) = e^(4πit): winds twice: [γ] = 2 ≠ 0! Can't contract to point (would unwind!)! Homotopy: continuous deformation! (Fundamental group counts holes!)