Geometric and arithmetic subgroups of the Grothendieck-Teichmüller group.
The Grothendieck-Teichmüller group \(\widehat{GT}\) is a subgroup of the automorphism group \(\Aut\widehat F_2\) of the free profinite group \(\widehat F_2\) of rank 2. \textit{Y. Ihara} [in: The Grothendieck theory of dessins d'enfants. Lond. Math. Soc. Lect. Note Ser. 200, 289--321 (1994; Zbl 0849.12005)] showed that the absolute Galois group \(\text{Gal}(\overline{\mathbb Q}/{\mathbb Q})\) can be embedded in \(\widehat{GT}\). It is still open whether \(\text{Gal} (\overline{\mathbb Q}/{\mathbb Q})\) is equal to \(\widehat{GT}\). In this article the author studies connections between several new-type relations satisfied by \(\text{Gal} (\overline{\mathbb Q}/{\mathbb Q})\) and \(\widehat{GT}\) that were discovered recently.
scientific article; zbMATH DE number 1918965