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Operads of genus zero
curves and the Grothendieck–Teichmüller group
Pedro Boavida de Brito, Geoffroy Horel and Marcy Robertson |
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Geometry & Topology 23 (2019) 299–346
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Abstract |
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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 , the operad of stable curves of genus zero. As a second application, we give an alternative proof that the framed little –disks operad is formal. |
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Keywords
infinity operads, Grothendieck–Teichmüller group, absolute
Galois group, moduli space of curves
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Mathematical Subject Classification 2010
Primary: 18D50, 14G32, 32G15, 55P48, 55U35
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References |
Publication
Received: 20 July 2017
Accepted: 13 July 2018
Published: 5 March 2019
Proposed: Ulrike Tillmann
Seconded: Haynes R Miller, Ralph Cohen
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Authors |
| Pedro Boavida de Brito | |
| Instituto Superior Técnico Universidade de Lisboa Lisboa Portugal |
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| Geoffroy Horel | |
| LAGA Institut Galilée Université Paris 13 Villetaneuse France |
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| Marcy Robertson | |
| School of Mathematics and
Statistics The University of Melbourne Melbourne Victoria Australia |
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