Operads of genus zero curves and the Grothendieck-Teichm\'{u}ller group

Autor:	de Brito, Pedro Boavida, Horel, Geoffroy, Robertson, Marcy
Rok vydání:	2017
Předmět:	Mathematics - Algebraic Topology Mathematics - Algebraic Geometry Mathematics - Quantum Algebra
Zdroj:	Geom. Topol. 23 (2019) 299-346
Druh dokumentu:	Working Paper
DOI:	10.2140/gt.2019.23.299
Popis:	We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichm\"{u}ller group. Using a result of Drummond-Cole, we deduce that the Grothendieck-Teichm\"{u}ller 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. Comment: 36 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.05143 Zobrazit plný text záznamu View this record from Arxiv