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Not all free arrangements are $ K(\pi,1)$

Authors: Paul H. Edelman and Victor Reiner
Journal: Bull. Amer. Math. Soc. 32 (1995), 61-65
MSC: Primary 52B30; Secondary 55P20
MathSciNet review: 1273396
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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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