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Profinite completion of operads and the Grothendieck-Teichmüller group (1504.01605v2)
Published 7 Apr 2015 in math.AT, math.AG, and math.QA
Abstract: In this paper, we prove that the group of homotopy automorphisms of the profinite completion of the operad of little $2$-disks is isomorphic to the profinite Grothendieck-Teichm\"uller group. In particular, the absolute Galois group of $\mathbb{Q}$ acts faithfully on the profinite completion of $E_2$ in the homotopy category of profinite weak operads.