Using the fundamental exact sequence of X = P^1\{0, 1, \infty}, one obtains an outer action of G_Q on pi_1^{alg}(X'), where X' is the base change of X to the algebraic closure of Q. In fact G_R can be recovered as the intersection of G_Q and Out(\pi_1^{top}(X'')), where X'' is the base change of X' to the complex numbers, fixing some embedding of the algebraic closure of Q into C. A paper of Yves Andre shows how to make an analogous construction to recover G_{Q_p} for any p. The construction uses the "Tempered Fundamental Group," which will be discussed in detail.