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aljungstrom committed Sep 11, 2024
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5 changes: 2 additions & 3 deletions Cubical/Homotopy/Group/Pi4S3/DirectProof.agda
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Expand Up @@ -18,9 +18,8 @@ complicates things. In this file, we try to work around this problem.
The proof goes as follows.
1. Define π₃*(A) := ∥ S¹ * S¹ →∙ A ∥₀ and define explicitly an
addition on this type. Prove that the equivalence π₃(A) ≃ π₃*(A) is
structure preserving, thereby giving a group structure on π₃*(A) and a
group iso π₃*(A) ≅ π₃(A)
addition on this type. This is already done in
Cubical.Homotopy.Group.Join.
2. Under this iso, η gets mapped to η₁ (by construction) defined by
S¹ * S¹ -ᵂ→ S² ∨ S² -ᶠᵒˡᵈ→ S²
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