44 citations · 148 across the 11 of their papers we have counts for
12 papers
Hopf algebras of multiple polylogarithms, and holomorphic 1-forms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that t…
The Lie coalgebra of multiple polylogarithms
Zachary Greenberg, Dani Kaufman, Haoran Li +1
We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, whic…
Holomorphic polylogarithms and Bloch complexes
Christian K. Zickert
For an integer n>2 we define a polylogarithm, which is a holomorphic function on the universal abelian cover of C-{0,1} defined modulo (2 pi i)^n/(n-1)!. We use the formal properti…
On the Hikami-Inoue conjecture
Jinseok Cho, Seokbeom Yoon, Christian K. Zickert
Given a braid presentation of a hyperbolic knot, Hikami and Inoue consider a system of polynomial equations arising from a sequence of cluster mutations determined by . They…
Fock-Goncharov coordinates for rank two Lie groups
Christian K. Zickert
Let G be a simply connected, simple, complex Lie group of rank 2. We give explicit Fock-Goncharov coordinates for configurations of triples and quadruples of affine flags in G. We…
Ptolemy coordinates, Dehn invariant, and the A-polynomial
Christian K. Zickert
We define Ptolemy coordinates for representations that are not necessarily boundary-unipotent. This gives rise to a new algorithm for computing the SL(2,C) A-polynomial, and more g…
The Ptolemy field of -manifold-representations
Stavros Garoufalidis, Matthias Goerner, Christian K. Zickert
The Ptolemy coordinates for boundary-unipotent SL(n,C)-representations of a 3-manifold group were introduced in Garoufalidis-Thurston-Zickert inspired by the A-coordinates on highe…
The symplectic properties of the PGL(n,C)-gluing equations
Stavros Garoufalidis, Christian K. Zickert
In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thur…
Gluing equations for PGL(n,C)-representations of 3-manifolds
Stavros Garoufalidis, Matthias Goerner, Christian K. Zickert
In a previous paper, we parametrized boundary-unipotent representations of a 3-manifold group into SL(n,C) using Ptolemy coordinates, which were inspired by A-coordinates on higher…
The extended Bloch group and algebraic K-theory
Christian K. Zickert
We define an extended Bloch group for an arbitrary field F, and show that this group is canonically isomorphic to K_3^ind(F) if F is a number field. This gives an explicit descript…
A dilogarithmic formula for the Cheeger-Chern-Simons class
Johan Dupont, Christian Zickert
We present a simplification of Neumann's formula for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final fo…
The volume and Chern-Simons invariant of a representation
Christian K. Zickert
We give an efficient simplicial formula for the volume and Chern-Simons invariant of a boundary-parabolic PSL(2,C)-representation of a tame 3-manifold. If the representation is the…