ar X iv : m at h / 05 08 06 6 v 1 [ m at h . N T ] 3 A ug 2 00 5 MULTIPLE POLYLOGARITHMS , POLYGONS , TREES AND ALGEBRAIC CYCLES
نویسندگان
چکیده
We construct, for a field F and a natural number n, algebraic cycles in Bloch's cubical cycle group of codimension n cycles in P 1 F \{1} 2n−1 , which correspond to weight n multiple polylogarithms with generic arguments if F ⊂ C. Moreover, we construct out of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra χ cycle. In the process, we are led to other Hopf algebras built from trees and polygons, which are mapped to χ cycle. We relate the coproducts to the one for Goncharov's motivic multiple polylogarithms and to the Connes-Kreimer coproduct on plane trees and produce the associated Hodge realization for polygons.
منابع مشابه
ar X iv : m at h / 05 04 55 2 v 1 [ m at h . N T ] 2 7 A pr 2 00 5 Multiple logarithms , algebraic cycles and trees
This is a short exposition—mostly by way of the toy models " double logarithm " and " triple logarithm " —which should serve as an introduction to the article [3] in which we establish a connection between multiple polylogarithms, rooted trees and algebraic cycles.
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