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Minor optimization.

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favonia 2017-06-09 15:55:19 -06:00
parent a78c92636e
commit 5d57e60a43
2 changed files with 5 additions and 2 deletions
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3
homology/homology.hlean
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@ -142,6 +142,9 @@ namespace homology
calc HH theory n (plift.{u v} (A ∨ B)) ≃g HH theory n (plift.{u v} A ∨ plift.{u v} B) : by exact HH_isomorphism theory n (plift_pwedge A B)
... ≃g HH theory n (plift.{u v} A) ×g HH theory n (plift.{u v} B) : by exact Hpwedge theory n (plift.{u v} A) (plift.{u v} B)
definition Hplift_isomorphism (n : ℤ) {A B : Type*} (e : A ≃* B) : HH theory n (plift.{u v} A) ≃g HH theory n (plift.{u v} B) :=
HH_isomorphism theory n (!pequiv_plift⁻¹ᵉ* ⬝e* e ⬝e* !pequiv_plift)
end
/- homology theory associated to a prespectrum -/

4
homology/torus.hlean
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@ -22,7 +22,7 @@ section
calc HH theory n (plift (psphere m ×* psphere m))
≃g HH theory (n + 1) (plift (⅀ (psphere m ×* psphere m))) : by exact (Hplift_psusp theory n (psphere m ×* psphere m))⁻¹ᵍ
... ≃g HH theory (n + 1) (plift (⅀ (psphere m) ∨ (⅀ (psphere m) ∨ ⅀ (psphere m ∧ psphere m))))
: by exact HH_isomorphism theory (n + 1) (!pequiv_plift⁻¹ᵉ* ⬝e* susp_product (psphere m) (psphere m) ⬝e* !pequiv_plift)
: by exact Hplift_isomorphism theory (n + 1) (susp_product (psphere m) (psphere m))
... ≃g HH theory (n + 1) (plift (⅀ (psphere m))) ×g HH theory (n + 1) (plift (⅀ (psphere m) ∨ (⅀ (psphere m ∧ psphere m))))
: by exact Hplift_pwedge theory (n + 1) (⅀ (psphere m)) (⅀ (psphere m) ∨ (⅀ (psphere m ∧ psphere m)))
... ≃g HH theory n (plift (psphere m)) ×g (HH theory n (plift (psphere m)) ×g HH theory n (plift (psphere (m + m))))
@ -33,7 +33,7 @@ section
: by exact Hplift_pwedge theory (n + 1) (⅀ (psphere m)) (⅀ (psphere m ∧ psphere m))
... ≃g HH theory n (plift (psphere m)) ×g HH theory n (plift (psphere (m + m)))
: by exact product_isomorphism (Hplift_psusp theory n (psphere m))
(Hplift_psusp theory n (psphere m ∧ psphere m) ⬝g HH_isomorphism theory n (!pequiv_plift⁻¹ᵉ* ⬝e* (sphere_smash_sphere m m) ⬝e* !pequiv_plift)))
(Hplift_psusp theory n (psphere m ∧ psphere m) ⬝g Hplift_isomorphism theory n (sphere_smash_sphere m m)))
end