Some classical views on the parameters of the Grothendieck-Teichmüller group

Abstract

We present two new formulas concerning behaviors of the standard parameters of the Grothendieck-Teichmüller group GT, and discuss their relationships with classical mathematics. First, considering a non-Galois etale cover of P1 - {0,1,∞} of degree 4, we present a newtype equation satisfied by the Galois image in GT. Second, a certain equation in GL2 (Z[[Z2]]) satisfied by every element of GT is derived as an application of (profinite) free differential calculus. © 2005 Springer Science + Business Media, Inc.