The Grothendieck-Teichmueller Lie algebra and Brown's dihedral moduli spaces

TL;DR

This paper establishes a precise algebraic relationship between the Hochschild cohomology of Brown's dihedral moduli spaces and the Grothendieck-Teichmueller Lie algebra, shedding light on their connection to multiple zeta values.

Contribution

It proves that the degree zero Hochschild cohomology of the homology operad of these moduli spaces equals the Grothendieck-Teichmueller Lie algebra plus two classes, clarifying their conjectural link.

Findings

Hochschild cohomology matches the Grothendieck-Teichmueller Lie algebra plus two classes

Provides evidence for the conjectural relation between motivic multiple zeta values and the Lie algebra

Advances understanding of the algebraic structures underlying moduli spaces

Abstract

We prove that the degree zero Hochschild-type cohomology of the homology operad of Francis Brown's dihedral moduli spaces is equal to the Grothendieck-Teichmueller Lie algebra plus two classes. This significantly elucidates the (in part still conjectural) relation between the Grothendieck-Teichmueller Lie algebra and (motivic) multiple zeta values.