IV.D361 — Fiber-Base Homology of τ³

H₁(τ³; ℤ) ≅ ℤ³ from the fiber-base decomposition τ³ = τ¹ ×_f T². The rank 3 = rank(H₁(T²)) + rank(H₁(τ¹)) = 2 + 1 is a topological invariant. Three independent generators: g₁ (meridian of T²), g₂ (longitude of T²), g₃ (base cycle of τ¹).