Homotopy invariance of the topological degree — unconditional #
Now that the singular prism operator is a theorem (singularPrismOperator,
established in SingularHomologyHomotopyInvariance.lean from the backported
algebraic prism and the library cylinder), the homotopy-invariance wrappers of
Degree.lean — which were stated conditionally on SingularPrismOperator — are
unconditional.
theorem
SphereOddDegree.inducedOnTopHomology_eq_of_homotopic_unconditional
{n : ℕ}
{f g : C(Sphere n, Sphere n)}
(h : f.Homotopic g)
:
Homotopy invariance of the induced top-homology endomorphism (unconditional).
Homotopic self-maps f, g : C(Sphere n, Sphere n) induce the same endomorphism of
Hₙ(TopCat.sphere n; ℤ).
theorem
SphereOddDegree.degreeOfIso_eq_of_homotopic_unconditional
{n : ℕ}
(e : (singularHomologyℤ n).obj (TopCat.sphere n) ≅ ↧ℤ)
{f g : C(Sphere n, Sphere n)}
(h : f.Homotopic g)
:
Homotopy invariance of the degree (unconditional).
Homotopic self-maps of Sphere n have equal degree relative to any chosen
identification e : Hₙ(Sⁿ; ℤ) ≅ ℤ.