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

Abstract

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

7 pages, 2 figures. Comments are welcome!