Abstract
Let A be an arrangement of complex hyperplanes and M A the complement of the union of hyperplanes in A . The Orlik–Solomon algebra of A determines a subcomplex of the de Rham complex of the loop space of M A , which is called the bar complex of the Orlik–Solomon algebra. The dual of this complex is isomorphic to the tensor algebra of the homology of M A equipped with a derivation arising from the product structure of the Orlik–Solomon algebra. Based on this construction we give an explicit description of Chen's iterated integrals of logarithmic forms depending only on the homotopy class of a loop.
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