21 citations · 54 across the 7 of their papers we have counts for
14 papers
Multiple polylogarithms, polygons, trees and algebraic cycles
Herbert Gangl, Alexander B. Goncharov, Andrey Levin
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 subalgebr…
Cluster X-varieties, amalgamation and Poisson-Lie groups
V. V. Fock, A. B. Goncharov
Starting from a split semisimple real Lie group G with trivial center, we define a family of varieties with additional structures. We describe them as the cluster X-varieties, as d…
Multiple logarithms, algebraic cycles and trees
Herbert Gangl, Alexander B. Goncharov, Andrey Levin
This is a short exposition--mostly by way of the toy models ``double logarithm'' and ``triple logarithm''--which should serve as an introduction to a forthcoming article in which w…
Moduli spaces of convex projective structures on surfaces
V. V. Fock, A. B. Goncharov
We define convex projective structures on 2D surfaces with holes and investigate their moduli space. We prove that this moduli space is canonically identified with the higher Teich…
Moduli spaces of local systems and higher Teichmuller theory
V. V. Fock, A. B. Goncharov
Let G be a split semisimple algebraic group with trivial center. Let S be a compact oriented surface, with or without boundary. We define {\it positive} representations of the fund…
Galois symmetries of fundamental groupoids and noncommutative geometry
A. B. Goncharov
We define motivic iterated integrals on the affine line, and give a simple proof of the formula for the coproduct in the Hopf algebra of they make. We show that it encodes the grou…