The $K(π,1)$ -conjecture implies the center conjecture for Artin groups

preprint2022arXivOpen access

In this note, we prove that the $K(π,1)$ -conjecture for Artin groups implies the center conjecture for Artin groups. Specifically, every Artin group without a spherical factor that satisfies the $K(π,1)$ -conjecture has a trivial center.

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The $K(π,1)$ -conjecture implies the center conjecture for Artin groups

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The K(π,1)K(π,1)K(π,1)-conjecture implies the center conjecture for Artin groups

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The $K(π,1)$ -conjecture implies the center conjecture for Artin groups