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?
2026-03-25 20:42:33.1774471353
Higher homotopy groups of the Klein bottle
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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.