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arXiv · 1504.01605

Profinite completion of operads and the Grothendieck-Teichm\"uller group

Geoffroy Horel
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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.

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BibTeXRIS

Geoffroy Horel. 2015-04-07. Profinite completion of operads and the Grothendieck-Teichm\"uller group. https://arxiv.org/abs/1504.01605

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