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

Abstract

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