Animation showing the homotopy equivalence between a solid torus with k points removed and a wedge sum of a circle and k 2-spheres. During the process we obtain a chain of spheres (S²) in a loop (pearl necklace / necklace with k beads). The chain is homotopic to a wedge sum of k spheres and a circle, and using van Kampen's theorem one may show that the fundamental group of the space is ℤ (π₁(S²) is trivial and π₁(S¹) is isomorphic to ℤ ).
Негізгі бет Solid torus without k points homotopy equivalence
Пікірлер: 10