On a subgroup of the Grothendieck-Teichmüller group acting on the tower of profinite Teichmüller modular groups. (Q1581816)

This paper is a major contribution to the study of the Grothendieck-Teichmüller group \(\widehat{GT}\). A new subgroup \(\Gamma\) of \(\widehat{GT}\) is introduced by adding two newtype relations. It is shown that the absolute Galois group of \(\mathbb Q\) still embeds in \(\Gamma\) (but no new results about whether \(G_{\mathbb Q} = \widehat{GT}\)). It is shown that \(\Gamma\) acts on all types of profinite Teichmüller modular groups \(\hat{\Gamma}^n_{g,m}\) in a consistent manner. The results are too technical to reproduce here.