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arXiv · 2309.02344

On the commutator length of compact Lie groups

Juan Omar Gómez·Victor Torres-Castillo·Bernardo Villarreal
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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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Juan Omar Gómez, Victor Torres-Castillo, Bernardo Villarreal. 2023-09-05. On the commutator length of compact Lie groups. https://arxiv.org/abs/2309.02344

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