Not all free arrangements are 𝐾(𝜋,1)

Edelman, Paul H.; Reiner, Victor

doi:10.1090/S0273-0979-1995-00557-4

Not all free arrangements are $K(\pi ,1)$
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by Paul H. Edelman and Victor Reiner PDF

Bull. Amer. Math. Soc. 32 (1995), 61-65 Request permission

Abstract:

We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is $K(\pi ,1)$. These arrangements are the restriction of a one-parameter family of arrangements that arose in the study of tilings of certain centrally symmetric octagons. This other family is discussed as well.

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