Multiple polylogarithms, polygons, trees and algebraic cycles

Details Multiple polylogarithms, polygons, trees and algebraic cycles Multiple polylogarithms, polygons, trees and algebraic cycles

2005-08-03

arxiv.org/abs/math/0508066v1

Mathematics

Number Theory

46 pages, figures use xy-pic

Scientific paper

We construct algebraic cycles in Bloch's cubical cycle group which correspond to multiple polylogarithms with generic arguments. Moreover, we construct out of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra. In the process, we are led to other Hopf algebras built from trees and polygons, which are mapped to the latter. 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.

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