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
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 ̄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.

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