### The Galois action on the torsor of homotopy classes of paths on a projective line minus a finite number of points, by Zdzislaw Wojtkowiak

We are studying the action of the Galois groups on torsors
of paths on a projective line minus several points. In case of
$\mathbb{P}^1 \setminus \{ 0, 1, \infty \}$ and a torsor of paths from
$\vec 01$ to $-1$ we showed that the Lie algebra of derivations
associated with the image of $Gal(\bar Q/Q_{\mu _{l^\infty }})$ is
free on generators in degre e $1,3,5,\ldots 2n+1,\ldots $. We use
result of Deligne concerning $\mathbb{P}^1 \setminus \{ 0, 1,-1,
\infty \}$.

Zdzislaw Wojtkowiak <wojtkow@math.unice.fr>