• Corpus ID: 119731329

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

@article{Alm2018TheGL,
title={The Grothendieck-Teichmueller Lie algebra and Brown's dihedral moduli spaces},
author={J. Alm},
journal={arXiv: Quantum Algebra},
year={2018}
}
• J. Alm
• Published 17 May 2018
• Mathematics
• arXiv: Quantum Algebra
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.
1 Citations

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## References

SHOWING 1-10 OF 16 REFERENCES

### Brown's moduli spaces of curves and the gravity operad

• Mathematics
• 2015
This paper is built on the following observation: the purity of the mixed Hodge structure on the cohomology of Brown's moduli spaces is essentially equivalent to the freeness of the dihedral operad

### Operads and Moduli Spaces of Genus 0 Riemann Surfaces

In this paper, we study two dg (differential graded) operads related to the homology of moduli spaces of pointed algebraic curves of genus 0. These two operads are dual to each other, in the sense of

### Operads and Motives in Deformation Quantization

The algebraic world of associative algebras has many deep connections with the geometric world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of chains of the little

### A Universal A∞ Structure on BV Algebras with Multiple Zeta Value Coefficients

We construct an explicit and universal A-infinity deformation of Batalin-Vilkovisky algebras, with all coefficients expressed as rational sums of multiple zeta values. If the Batalin-Vilkovisky alg

### Relative (non-)formality of the little cubes operads and the algebraic Cerf lemma

• Mathematics
• 2014
abstract:It is shown that the operad maps $E_n\to E_{n+k}$ are formal over the reals for $k\geq 2$ and non-formal for $k=1$. Furthermore we compute the homology of the deformation complex of the

### Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves M_g,n

• Mathematics
• 2015
We establish a new and surprisingly strong link between two previously unrelated theories: the theory of moduli spaces of curves Mg,n (which, according to Penner, is controlled by the ribbon graph

### Mixed Tate motives over $\Z$

We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every

### M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra

We show that the zeroth cohomology of M. Kontsevich’s graph complex is isomorphic to the Grothendieck–Teichmüller Lie algebra $$\mathfrak {{grt}}_1$$grt1. The map is explicitly described. This result

### Brown's dihedral moduli space and freedom of the gravity operad

• Mathematics
• 2015
Francis Brown introduced a partial compactification $M_{0,n}^\delta$ of the moduli space $M_{0,n}$. We prove that the gravity cooperad, given by the degree-shifted cohomologies of the spaces

### Pentagon and hexagon equations

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