A sphere with 2 points identified is homotopy equivalent to a wedge sum of a sphere and a circle. Two possible visualizations are presented in this video. Illustrated homotopy equivalence helps us find the fundamental group of S²/S⁰- it is ℤ, since π₁(S² ∨ S¹) is isomorphic to ℤ.
More generally, a sphere with k points identified is homotopy equivalent to a wedge sum of a sphere and (k-1) circles.
Негізгі бет Sphere with 2 points identified homotopy equivalence
Пікірлер: 10