Given a compact oriented surface \(\Sigma\) of genus \(g\) with one boundary component, and with basepoint \(p_0\in \partial \Sigma\), the mapping class group \(\mathcal{M}_{g,1}=\pi_0(\mathrm{Diff}_+(\Sigma,\partial \Sigma))\) of \((\Sigma,\partial \Sigma)\), where \(\mathrm{Diff}_+(\Sigma,\partial \Sigma)\) is the group of orientation preserving diffeomorphisms of \(\Sigma\) restricting to the identity on \(\partial \Sigma\), naturally acts on the (co)homology of the configuration space of points of \(\Sigma\).
The paper contains two main results on this action. The first one states that the kernel of the natural action of \(\mathcal{M}_{g,1}\) on the cohomology of the configuration space of \(n\)-points of \(\Sigma-\{p_0\}\) coincides with the kernel of the natural action on the \(n\)th lower central quotient group \(\Gamma_0/\Gamma_n\), \(\Gamma_0\) being \(\pi_1(\Sigma,p_0)\). The second result is obtained constructing a certain cochain complex \(C\) of \(\mathcal{M}_{g,1}\)-modules, whose coboundary maps represent how points on \(\Sigma\) make collisions with each other. It is shown that the cohomology of \(\mathcal{M}_{g,1}\) with coefficients in the tensor algebra \(T(H_1)\) of \(H_1(\Sigma;\mathbb{Z})\) is isomorphic to the cohomology of \(\mathcal{M}_{g,1}\) with coefficients in \(C\), yielding a new interpretation of \(H^*(\mathcal{M}_{g,1};T(H_1))\) by using the configuration spaces.