• Corpus ID: 220041667

Dessins for Modular Operad and Grothendieck-Teichmuller Group

@article{Combe2020DessinsFM,
  title={Dessins for Modular Operad and Grothendieck-Teichmuller Group},
  author={Noemie C. Combe and Yu. I. Manin and Matilde Marcolli},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
A part of Grothendieck's program for studying the Galois group $G_{\mathbb Q}$ of the field of all algebraic numbers $\overline{\mathbb Q}$ emerged from his insight that one should lift its action upon $\overline{\mathbb Q}$ to the action of $G_{\mathbb Q}$ upon the (appropriately defined) profinite completion of $\pi_1({\mathbb P}^1 \setminus \{0,1, \infty\})$. The latter admits a good combinatorial encoding via finite graphs "dessins d'enfant". This part was actively developing during the… 
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References

SHOWING 1-10 OF 32 REFERENCES
New moduli spaces of pointed curves and pencils of flat connections.
It is well known that formal solutions to the Associativity Equations are the same as cyclic algebras over the homology operad $(H_*(\bar{M}_{0,n+1}))$ of the moduli spaces of $n$--pointed stable
Operads of genus zero curves and the Grothendieck–Teichmüller group
We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichm\"{u}ller group. Using a result of
The Grothendieck theory of dessins d'enfants
1. Noncongruence subgroups, covers, and drawings B. Birch 2. Dessins d'enfant on the Riemann sphere L. Schneps 3. Dessins from a geometric point of view J-M. Couveignes and L. Granboulan 4. Maps,
Genus zero modular operad and absolute Galois group
In this article, we develop the geometry of canonical stratifications of the spaces $\overline{\mathcal{M}}_{0,n}$ and prepare ground for studying the action of the Galois group
Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
In this paper, we construct a naturalC*-dynamical system whose partition function is the Riemann ζ function. Our construction is general and associates to an inclusion of rings (under a suitable
Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem
Abstract:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure
Symmetries of genus zero modular operad
In this article combining survey and certain research results, we introduce a categorical framework for description of symmetries of genus zero modular operad. This description merges the techniques
Gromov-Witten classes, quantum cohomology, and enumerative geometry
The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic
Dendroidal Segal spaces and ∞‐operads
We introduce the dendroidal analogues of the notions of complete Segal space and of Segal category, and construct two appropriate model categories for which each of these notions corresponds to the
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