Multiple polylogarithms, polygons, trees and algebraic cycles

Gangl, Herbert; Goncharov, Alexander B.; Levin, Andrey

Multiple polylogarithms, polygons, trees and algebraic cycles

Authors

Gangl, Herbert

Goncharov, Alexander B.

Levin, Andrey

Description

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.
46 pages, figures use xy-pic