How would you show that $\pi_n, n>1$ of the Klein bottle is the trivial group?
I was thinking Seifert-Van Kampen could be applicable?
How would you show that $\pi_n, n>1$ of the Klein bottle is the trivial group?
I was thinking Seifert-Van Kampen could be applicable?
The universal cover of the Klein bottle is $\mathbb{R}^2$. You can use lifting criteria from covering space theory to show that the Klein bottle and its covering spaces have the same higher homotopy groups.