Multiple polylogarithms, polygons, trees and algebraic cycles
数论
2007-05-23 v1 代数几何
组合数学
摘要
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.
引用
@article{arxiv.math/0508066,
title = {Multiple polylogarithms, polygons, trees and algebraic cycles},
author = {Herbert Gangl and Alexander B. Goncharov and Andrey Levin},
journal= {arXiv preprint arXiv:math/0508066},
year = {2007}
}
备注
46 pages, figures use xy-pic