The Grothendieck-Teichm\"uller group $\widehat{GT}$ acts on the genus $g$ mapping class group with $0$ or $1$ marked point

Pierre Lochak; Hiroaki Nakamura; Leila Schneps

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arXiv · 2602.12462

The Grothendieck-Teichm\"uller group $\widehat{GT}$ acts on the genus $g$ mapping class group with $0$ or $1$ marked point

Pierre Lochak·Hiroaki Nakamura·Leila Schneps

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Abstract

The goal of this article is to prove that the Grothendieck-Teichm\"uller group $\widehat{GT}$ acts on $\widehat{\Gamma}_{g,0}$ and $\widehat{\Gamma}_{g,1}$,the (full) profinite genus $g$ mapping class group with $0$ or $1$ marked point, for every $g>0$.

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Pierre Lochak, Hiroaki Nakamura, Leila Schneps. 2026-02-12. The Grothendieck-Teichm\"uller group $\widehat{GT}$ acts on the genus $g$ mapping class group with $0$ or $1$ marked point. https://arxiv.org/abs/2602.12462

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