Operads of genus zero curves and the Grothendieck-Teichmüller group

Abstract

We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichmüller group. Using a result of Drummond-Cole, we deduce that the Grothendieck-Teichmüller group acts nontrivially on ${\overline{\mathcal{M}}}_{0,\bullet +1}$, the operad of stable curves of genus zero. As a second application, we give an alternative proof that the framed little 2-disks operad is formal.

36 pages

References in corpus (1)

• Higher Topos Theory

Cited by in corpus (10)

• A graphical category for higher modular operads
• Etale cohomology, purity and formality with torsion coefficients
• Quantum Statistical Mechanics of the Absolute Galois Group
• A spectral sequence for spaces of maps between operads
• Genus zero modular operad and absolute Galois group
• Toward a Galois theory of the integers over the sphere spectrum
• Simplicial model structures on pro-categories
• An infinity operad of normalized cacti
• Surface Drinfeld Torsors I : Higher Genus Associators
• Profinite $\infty$-operads