Formal weights in Kontsevich's formality construction and multiple zeta values

TL;DR

This paper develops a functorial construction linking dg cooperads to augmented commutative algebras, providing a formal model for multiple zeta values and revealing structural connections with the Grothendieck-Teichmüller Lie algebra.

Contribution

It introduces a new functorial framework connecting dg cooperads to algebras modeling multiple zeta values, and establishes key injections and surjections related to the Grothendieck-Teichmüller Lie algebra.

Findings

Injection from the dual of the Grothendieck-Teichmüller Lie algebra into indecomposables

Surjective morphism from Brown's moduli space algebra to the Gerstenhaber cooperad algebra

Formal modeling of multiple zeta values via constructed algebraic structures

Abstract

We construct a functor that associates to any dg cooperad of dg commutative algebras (satisfying some conditions) an augmented commutative algebra. When applied to the cohomology operad of Francis Brown's moduli spaces it produces an algebra that formally models the algebra of multiple zeta values. We prove that there is an injection from the graded dual of the Grothendieck-Teichmueller Lie algebra into the indecomposables of the algebra associated to the Gerstenhaber cooperad, and that there is a morphism from the algebra associated to Brown's moduli spaces to the algebra associated to the Gerstenhaber cooperad which is surjective on indecomposables.