MOORE AND SEIBERG EQUATIONS, TOPOLOGICAL THEORIES AND GALOIS THEORY

We recall the construction of a three-dimensional projective topologic al field theory starting from a solution to Moore and Seiberg equation s. The conjectural relation between Moore and Seiberg's equations and the second paragraph of the ''Esquisse d'un programme'' by A. Grothend ieck is discussed. Then, following Grothendieck's ideas, we suggest ho w to translate Gal((Q) over bar/Q)'s natural action on pi(1)(alg)(P-1( C)\ {0,1, infinity}, ) into an explicit action on a wide class of top ological field theories deduced from two-dimensional rational conforma l field theories.