On the commutator length of compact Lie groups

Published 5 Sep 2023 in math.GR and math.AT | (2309.02344v1)

Abstract: In this short note we show that the path-connected component of the identity of the derived subgroup of a compact Lie group consists just of commutators. We also discuss an application of our main result to the homotopy type of the classifying space for commutativity for a compact Lie group whose path-connected component of the identity is abelian.

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