グロタンディーク・タイヒミューラー群と関連したある直積分解について (Algebraic Number Theory and Related Topics 2017)

Abstract

In this article, we announce our results on the Grothendieck-Teichmüller group GT obtained in the joint work with Yuichiro Hoshi and Shinichi Mochizuki. Let n ≥ 2 be a positive integer and k an algebraically closed field of characteristic zero. Write IIn for the étale fundamental group of the n-th configuration space of P1 k/{0, 1, 1∞} and Sn+3 for the symmetric group on n + 3 letters. Then our main theorem asserts that we have a direct product decomposition Out(IIn) = GT × Sn+3. The detail of the arguments appearing in this article may be found in [2].