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- W2054247743 abstract "Let ${mathcal {M}}_{0,n}$ denote the moduli space of Riemann spheres with $n$ ordered marked points. In this article we define the group $operatorname {Out}^{sharp }_{n}$ of quasi-special symmetric outer automorphisms of the algebraic fundamental group $widehat pi _{1}({mathcal {M}}_{0,n})$ for all $nge 4$ to be the group of outer automorphisms respecting the conjugacy classes of the inertia subgroups of $widehat pi _{1}({mathcal {M}}_{0,n})$ and commuting with the group of outer automorphisms of $widehat pi _{1}({mathcal {M}}_{0,n})$ obtained by permuting the marked points. Our main result states that $operatorname {Out}^{sharp }_{n}$ is isomorphic to the Grothendieck-Teichmüller group $widehat {operatorname {GT}}$ for all $nge 5$." @default.
- W2054247743 created "2016-06-24" @default.
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- W2054247743 date "2000-03-31" @default.
- W2054247743 modified "2023-09-24" @default.
- W2054247743 title "Fundamental groups of moduli and the Grothendieck-Teichmüller group" @default.
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- W2054247743 doi "https://doi.org/10.1090/s0002-9947-00-02347-3" @default.
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