Volume 23, issue 1 (2019)

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Operads of genus zero curves and the Grothendieck–Teichmüller group

Pedro Boavida de Brito, Geoffroy Horel and Marcy Robertson

Geometry & Topology 23 (2019) 299–346

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 ̄0,+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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infinity operads, Grothendieck–Teichmüller group, absolute Galois group, moduli space of curves
Mathematical Subject Classification 2010
Primary: 18D50, 14G32, 32G15, 55P48, 55U35
Received: 20 July 2017
Accepted: 13 July 2018
Published: 5 March 2019
Proposed: Ulrike Tillmann
Seconded: Haynes R Miller, Ralph Cohen
Pedro Boavida de Brito
Instituto Superior Técnico
Universidade de Lisboa
Geoffroy Horel
Institut Galilée
Université Paris 13
Marcy Robertson
School of Mathematics and Statistics
The University of Melbourne