Mapping class group and the configuration space of surfaces.

We study the action of the mapping class group $\M_{g,1}$ on the
(co)homology groups of the configuration spaces of $n$-points on a
surface $\Sigma$ of genus $g$ with the boundary $\partial \Sigma \cong
S^1$.
We present two results in this talk. The first result is that the
kernel of the action of $M_{g,1}$ coincides with the kernel of the
natural action on the $n$-th lower central quotient group of the
fundamental group of $\Sigma$.
The second result is a new interpretation of the cohomology group
$H^*(M_{g,1},T[H_1])$ of $M_{g,1}$ with coefficients in the free
tensor algebra $T[H_1]$ over $Z$ generated by the first homology
group $H_1$ of $\Sigma$, by using the configuration spaces.