Geometric and arithmetic subgroups of the Grothendieck-Teichmüller group

We compare two geometrically constructed subgroups $\mathrm{I}\!\Gamma$ and $GTK$ of the Grothendieck-Teichmüller group $\widehat{GT}$ with an arithmetically constructed subgroup $GTA$ by deducing arithmetic properties from geometric ones. We show that the intersection of $\mathrm{I}\!\Gamma$ and $GTK$ is contained in a certain modification of $GTA$.

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Published 1 January 2003