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arXiv · 1703.05143

Operads of genus zero curves and the Grothendieck-Teichmüller group

Pedro Boavida de Brito·Geoffroy Horel·Marcy Robertson
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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.

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Pedro Boavida de Brito, Geoffroy Horel, Marcy Robertson. 2017-03-15. Operads of genus zero curves and the Grothendieck-Teichmüller group. https://doi.org/10.2140/gt.2019.23.299

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