3-nilpotent obstructions to pi_1 sections for P^1_Q - {0,1,infty}

Abstract: We study which rational points of the Jacobian of P^1_K -{0,1,infty} can be lifted to sections of geometrically 3 nilpotent quotients of etale pi_1 over the absolute Galois group. This is equivalent to evaluating certain triple Massey products of elements of H^1(G_K). For K=Q_p or R, we give a complete mod 2 calculation. This permits some mod 2 calculations for K = Q. These are computations of obstructions of Jordan Ellenberg.