Mathematical Research Letters

Volume 14, Issue 6, November 2007 pp. 923-942.

Algebraic Cycles and Motivic Generic Iterated Integrals

Authors: Hidekazu Furusho (1) and Amir Jafari (2)
Author institution: Nagoya University (1) and Duke University (2)

Summary: Following \cite{GGL}, we will give a combinatorial framework for motivic study of iterated integrals on the affine line. We will show that under a certain genericity condition these combinatorial objects yield to elements in the motivic Hopf algebra constructed in \cite{BK}. It will be shown that the Hodge realization of these elements coincides with the Hodge structure induced from the fundamental torsor of path of punctured affine line.

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