A sphere with k points removed is homotopy equivalent to a bouquet (or a wedge sum) of k-1 circles.
From the previous video we've seen that a k-punctured plane is homotopic to a wedge sum of k circles: kzitem.info/news/bejne/tqGIsaCHnaSfoII
One may also notice, that previous statement easily follows from current statement, since k-punctured sphere can be deformed to a (k-1)-punctured plane through a stereographic projection.
More generally, Sⁿ without k points is homotopy equivalent to a wedge sum of (k-1) copies of Sⁿ⁻¹.
Негізгі бет Bouquet of circles and sphere with k punctures homotopy equivalence
Пікірлер: 8