论文标题
Grothendieck的隐藏对称性 - TeichmüllerGroup
Hidden symmetries of the Grothendieck--Teichmüller group
论文作者
论文摘要
我们考虑了Grothendieck-Teichmüller集团在一个新方面。使用真实的代数几何和Web理论，我们表明它保留了二面体对称性关系，该关系中存在于$ \ Mathbb {c} $上的标记点的配置空间的基本群体中。本文的动机是根据格罗伦迪克（Grothendieck）的最初哲学来理解的，表明在整个曲线模量空间的隐藏对称性中，人们可以对绝对的galois群体阐明。这似乎是Grothendieck-TeichmüllerGroup的化身建设的新发展，并为研究与动机Galois集团的进一步关系做准备。
We consider the Grothendieck--Teichmüller group under a new aspect. Using real algebraic geometry and web theory we show that it preserves dihedral symmetry relations, present in the fundamental groupoids of configuration spaces of marked points on $\mathbb{C}$. The motivation of this paper is to be understood in the light of Grothendieck's initial philosophy stating that throughout hidden symmetries of the moduli spaces of curves one can shed some light on the absolute Galois group. This appears as a new development of the construction of the avatar of the Grothendieck--Teichmüller group and prepares as well the ground for studying further relations to the motivic Galois group.
