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$K(\pi,1)$-conjecture ofr Artin groups behave well with respect to special subgroups. Refere...
Yes, it has been proved by Godelle and Paris, it is cited as Theorem 5.5 in the article https://arxiv.org/pdf/1211.7339 by Paris (and Theorem 3.1 for the equivalence with the K(pi,1) conjecture).