Talk:String group

Dimension restriction

I think, this needs a dimension restriction of at least $n\geq 3$. Otherwise $Spin(n)$ is a point or circle implying that it does not have a third homotopy group to be killed. — Preceding unsigned comment added by 2A00:1398:9:FB03:DD1E:DEBC:DD79:8DD0 (talk) 14:16, 15 October 2019 (UTC)

There seems to be an obvious counterexample since $\pi_3 (S^1 \times S^1)$ is trivial, for compact Lie group — Preceding unsigned comment added by Niesocja (talk • contribs) 15:01, 1 September 2025 (UTC)