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The cohomology ring of the complement of a central complex hy- perplane arrangement is the well-studied Orlik-Solomon algebra. The homo- topy group of the complement is interesting, complicated, and few results are known about it. We study the ranks for the lower central series of such a ho- motopy group via the linear strand of the minimal free resolution of the eld C over the Orlik-Solomon algebra.

Hyperplane arrangements and linear strands in resolutions