The nonzero variation class over Γ_A #
Assembling the ledger identity with the prop_5_15 self-duality: from NoDescent, there is a
crossed T-cocycle u whose variation class [varCoc u] ∈ H²(Γ_A, 𝔽₂) is nonzero. This is the
hvar input to the abstract half-torsor count CentralObstruction.n (the Γ_A half-torsor proof).
The nonzero variation class over Γ_A (the Γ_A half-torsor proof). For a lower epimorphism ρ : Γ_A ↠ B/M
with nonzero radical edge (NoDescent), there is a crossed T-cocycle u whose variation class
is a nonzero element of H²(Γ_A, 𝔽₂).
#H²(Γ_A, 𝔽₂) = 2 (the Γ_A half-torsor proof hcard). The obstruction injection obsH2 : H² ↪ 𝔽₂ (c2)
gives ≤ 2; the nonzero variation class makes it surjective, hence a bijection.
Lemma 8.6, Γ_A source (the Γ_A half-torsor proof): with a nonzero radical edge, exactly half of the
unrestricted M-lifts of a lower epimorphism ρ : Γ_A ↠ B/M satisfy the central relation.
The abstract half-count CentralObstruction.half_count fed by the nonzero variation class
(exists_nonzero_varCoc_gammaA) and #H² = 2 (card_H2_gammaA_eq_two); the counted lift set is
finite because Γ_A is topologically finitely generated.
Paper-tag ledger (auto-generated by paperforge; do not edit) #
- Lemma 8.6 = ⟦lem-radicaledge⟧