Abstract
In this note we introduce and prove a wide generalization and sharpening of Ihara’s question / Oda–Matsumoto conjecture, for short I/OM. That leads to a quite concrete topological/combinatorial description of absolute Galois groups, in particular of $$\mathrm{Gal}_{{\mathbb {Q}}}=\mathrm{Aut}(\overline{{\mathbb {Q}}})$$ , as envisioned by Grothendieck in his Esquisse d’ un Programme.
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