Fundamental groups of moduli and the Grothendieck-Teichmüller group
Fundamental groups of moduli and the Grothendieck-Teichmüller group
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模的基本群和 Grothendieck-Teichmüller 群
DOI：
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发表时间：
2000
期刊：
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通讯作者：
Leila Schneps
中科院分区：
文献类型：
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作者：
D. Harbater;Leila Schneps
令Mo，表示有n个有序标记点的黎曼球的模空间。本文定义了所有n bbbb4的代数基本群1r1（Mo,n）的拟特对称外自同构群Out#是关于Irl（M4,n）的惯性子群的共轭类的外自同构群，并与通过置换标记点得到的rl（Mo,n）的外自同构群交换。我们的主要结果表明，对于所有的n - bbbb5， Outd与Grothendieck-Teichmiiller群GT是同构的。
Let Mo,, denote the moduli space of Riemann spheres with n ordered marked points. In this article we define the group Out# of quasispecial symmetric outer automorphisms of the algebraic fundamental group 1r1(Mo,n) for all n > 4 to be the group of outer automorphisms respecting the conjugacy classes of the inertia subgroups of Irl(M4,n) and commuting with the group of outer automorphisms of rl (MO,n) obtained by permuting the marked points. Our main result states that Outd is isomorphic to the Grothendieck-Teichmiiller group GT for all n > 5.